In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
Prunus serotina and Robinia pseudoacacia are the most widespread invasive trees in Central Europe.In addition,according to climate models,decreased growth of many economically and ecologically important native trees w...Prunus serotina and Robinia pseudoacacia are the most widespread invasive trees in Central Europe.In addition,according to climate models,decreased growth of many economically and ecologically important native trees will likely be observed in the future.We aimed to assess the impact of these two neophytes,which differ in the biomass range and nitrogen-fixing abilities observed in Central European conditions,on the relative aboveground biomass increments of native oaks Qucrcus robur and Q.petraea and Scots pine Pinus sylvestris.We aimed to increase our understanding of the relationship between facilitation and competition between woody alien species and overstory native trees.We established 72 circular plots(0.05 ha)in two different forest habitat types and stands varying in age in western Poland.We chose plots with different abundances of the studied neophytes to determine how effects scaled along the quantitative invasion gradient.Furthermore,we collected growth cores of the studied native species,and we calculated aboveground biomass increments at the tree and stand levels.Then,we used generalized linear mixed-effects models to assess the impact of invasive species abundances on relative aboveground biomass increments of native tree species.We did not find a biologically or statistically significant impact of invasive R.pseudoacacia or P.serotina on the relative aboveground,biomass increments of native oaks and pines along the quantitative gradient of invader biomass or on the proportion of total stand biomass accounted for by invaders.The neophytes did not act as native tree growth stimulators but also did not compete with them for resources,which would escalate the negative impact of climate change on pines and oaks.The neophytes should not significantly modify the carbon sequestration capacity of the native species.Our work combines elements of the per capita effect of invasion with research on mixed forest management.展开更多
In this paper,we prove some limsup results for increments and lag increments of G(t),which is a stable processe in random scenery.The proofs rely on the tail probability estimation of G(t).
As a data-driven approach, Deep Learning(DL)-based fault diagnosis methods need to collect the relatively comprehensive data on machine fault types to achieve satisfactory performance. A mechanical system may include ...As a data-driven approach, Deep Learning(DL)-based fault diagnosis methods need to collect the relatively comprehensive data on machine fault types to achieve satisfactory performance. A mechanical system may include multiple submachines in the real-world. During condition monitoring of a mechanical system, fault data are distributed in a continuous flow of constantly generated information and new faults will inevitably occur in unconsidered submachines, which are also called machine increments. Therefore, adequately collecting fault data in advance is difficult. Limited by the characteristics of DL, training existing models directly with new fault data of new submachines leads to catastrophic forgetting of old tasks, while the cost of collecting all known data to retrain the models is excessively high. DL-based fault diagnosis methods cannot learn continually and adaptively in dynamic environments. A new Continual Learning Fault Diagnosis method(CLFD) is proposed in this paper to solve a series of fault diagnosis tasks with machine increments. The stability–plasticity dilemma is an intrinsic issue in continual learning. The core of CLFD is the proposed Dual-branch Adaptive Aggregation Residual Network(DAARN).Two types of residual blocks are created in each block layer of DAARN: steady and dynamic blocks. The stability–plasticity dilemma is solved by assigning them with adaptive aggregation weights to balance stability and plasticity, and a bi-level optimization program is used to optimize adaptive aggregation weights and model parameters. In addition, a feature-level knowledge distillation loss function is proposed to further overcome catastrophic forgetting. CLFD is then applied to the fault diagnosis case with machine increments. Results demonstrate that CLFD outperforms other continual learning methods and has satisfactory robustness.展开更多
In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments fo...In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen＇s law of iterated logarithm for a Wiener process.展开更多
In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i...In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.展开更多
Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha...Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.展开更多
Let be a stable subordinator defined on a probability space and let at for t>0?be a non-negative valued function. In this paper, it is shown that under varying conditions on at, there exists a function such that wh...Let be a stable subordinator defined on a probability space and let at for t>0?be a non-negative valued function. In this paper, it is shown that under varying conditions on at, there exists a function such that where , , and .展开更多
Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discu...Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.展开更多
A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up a...A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up and then experimentally verified.And the relation between depth increment and the minimum thickness tmin as well as its location was analyzed through the FEM model.Afterwards,the variation of depth increments was defined.The designed part was divided into three areas according to the main deformation mechanism,with Di(i=1,2) representing the two dividing locations.And three different values of depth increment,Δzi(i=1,2,3) were utilized for the three areas,respectively.Additionally,an orthogonal test was established to research the relation between the five process parameters(D and Δz) and tmin as well as its location.The result shows that Δz2 has the most significant influence on the thickness distribution for the corresponding area is the largest one.Finally,a single evaluating indicator,taking into account of both tmin and its location,was formatted with a linear weighted model.And the process parameters were optimized through a genetic algorithm integrated with an artificial neural network based on the evaluating index.The result shows that the proposed algorithm is satisfactory for the optimization of variable depth increment.展开更多
Mid-subtropical forests are the main vegetation type of global terrestrial biomes, and are critical for maintaining the global carbon balance. However, estimates of forest biomass increment in mid-subtropical forests ...Mid-subtropical forests are the main vegetation type of global terrestrial biomes, and are critical for maintaining the global carbon balance. However, estimates of forest biomass increment in mid-subtropical forests remain highly uncertain. It is critically important to determine the relative importance of different biotic and abiotic factors between plants and soil, particularly with respect to their influence on plant regrowth. Consequently,it is necessary to quantitatively characterize the dynamicspatiotemporal distribution of forest carbon sinks at a regional scale. This study used a large, long-term dataset in a boosted regression tree（BRT） model to determine the major components that quantitatively control forest biomass increments in a mid-subtropical forested region（Wuyishan National Nature Reserve, China）. Long-term,stand-level data were used to derive the forest biomass increment, with the BRT model being applied to quantify the relative contributions of various biotic and abiotic variables to forest biomass increment. Our data show that total biomass（t） increased from 4.62 9 106 to 5.30 9 106 t between 1988 and 2010, and that the mean biomass increased from 80.19 ± 0.39 t ha-1（mean ± standard error） to 94.33 ± 0.41 t ha-1in the study region. The major factors that controlled biomass（in decreasing order of importance） were the stand, topography, and soil. Stand density was initially the most important stand factor, while elevation was the most important topographic factor. Soil factors were important for forest biomass increment but have a much weaker influence compared to the other two controlling factors. These results provide baseline information about the practical utility of spatial interpolationmethods for mapping forest biomass increments at regional scales.展开更多
A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-...A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.展开更多
Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all...Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1 983展开更多
In this paper,the models of increment distributions of stock price are constructed with two approaches. The first approach is based on limit theorems of random summation. The second approach is based on the statistica...In this paper,the models of increment distributions of stock price are constructed with two approaches. The first approach is based on limit theorems of random summation. The second approach is based on the statistical analysis of the increment distribution of the logarithms of stock prices.展开更多
Context and background: A quantum formulation of vision in vertebrates was proposed in the early 1940s. The number of quanta useful for enabling vision was found. The time interval required for their absorption, howev...Context and background: A quantum formulation of vision in vertebrates was proposed in the early 1940s. The number of quanta useful for enabling vision was found. The time interval required for their absorption, however, was never specified. In the early 1950s, experimental data on the effects of light’s intensity increment on vision indicated that the quantum formulation is true only at low light’s intensities. In this case, a vaguely described signaling adaptation mechanism was invoked to explain the separation between vision at low and high intensities, accompanied by the switch from rod to cones as photoreceptors. Motivation: In this article, we want to prove the validity of the non-totally-quantum formulation and unveil the nature of the signaling adaptation mechanism. Hypothesis: To accomplish our proof, we hypothesize that the amount of energy transferred and conserved in light’s interaction with the eyes is given by the product of light’s intensity (or power) times its period. Method: We construct and use the plots of the trends of light’s intensity increments and the corresponding changes in the axon’s membrane capacitance versus adapting intensity. Results: We find that 1) the average solar light’s intensity is the critical value that separates low from high light’s intensity regimes in vision, and 2) changes in the capacitance of the axon’s membrane enable the signaling adaptation of vision when light’s intensity changes. Conclusions: We prove the validity of the non-totally-quantum formulation and unveil the nature of the signaling adaptation mechanism. Our proof is supported by the model based on light’s intensity times period as being the energy conserved in light-matter interaction This model suggests that 1) all the waves in the electromagnetic spectrum, at the correct intensity for each frequency, could be used to produce the effects of optogenetics in diagnostics and therapy, and 2) it takes seconds to minutes to see details in the dark when light is switched off.展开更多
With the help of large deviation of Brownian motion in the Hölder norm,local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated.This paper promot...With the help of large deviation of Brownian motion in the Hölder norm,local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated.This paper promotes the corresponding results by Gantert and Wei.展开更多
Let X={X(t),t∈R+} be a centered space anisotropic Gaussian process values in R^(d) with non-stationary increments,whose components are independent but may not be identically distributed.Under certain conditions,then ...Let X={X(t),t∈R+} be a centered space anisotropic Gaussian process values in R^(d) with non-stationary increments,whose components are independent but may not be identically distributed.Under certain conditions,then almost surely c_(1)≤ϕ-m(X([0,1]))≤c_(2),where ϕ denotes the exact Hausdorff measure associated with function ϕ(s)=s1/α_(k)+Σ_(i=1)k(1-αi/αk)log log 1/s for some 1≤k≤d,(α_(1),…,α_(d))∈(0,1]^(d).We also obtain the exact Hausdorff measure of the graph of X on[0,1].展开更多
In this paper,we obtain the quasi sure local Chung’s functional law of the iterated logarithm for increments of a Brownian motion.As an application,a quasi sure Chung’s type functional modulus of continuity for a Br...In this paper,we obtain the quasi sure local Chung’s functional law of the iterated logarithm for increments of a Brownian motion.As an application,a quasi sure Chung’s type functional modulus of continuity for a Brownian motion is also derived.展开更多
A relationship was discovered between the amplification factor and the number of load increments that are needed to limit the relative error to one percent in second-order elastic analyses with a predictor-corrector s...A relationship was discovered between the amplification factor and the number of load increments that are needed to limit the relative error to one percent in second-order elastic analyses with a predictor-corrector solution scheme.Previous research by the authors proposed a design equation to determine the required minimum number of load increments based on an evaluation of the elastic critical buckling load ratio.Further research has shown that an approximate amplification factor equation that is based on the B2 multiplier equation produces similar results when the amplification factor is less than approximately four.Eleven moment frames are used to verify the use of the new approximate amplification factor in the proposed design equation.展开更多
In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
基金financed by the National Science Centre,Poland,under project No.2019/35/B/NZ8/01381 entitled"Impact of invasive tree species on ecosystem services:plant biodiversity,carbon and nitrogen cycling and climate regulation"by the Institute of Dendrology,Polish Academy of Sciences。
文摘Prunus serotina and Robinia pseudoacacia are the most widespread invasive trees in Central Europe.In addition,according to climate models,decreased growth of many economically and ecologically important native trees will likely be observed in the future.We aimed to assess the impact of these two neophytes,which differ in the biomass range and nitrogen-fixing abilities observed in Central European conditions,on the relative aboveground biomass increments of native oaks Qucrcus robur and Q.petraea and Scots pine Pinus sylvestris.We aimed to increase our understanding of the relationship between facilitation and competition between woody alien species and overstory native trees.We established 72 circular plots(0.05 ha)in two different forest habitat types and stands varying in age in western Poland.We chose plots with different abundances of the studied neophytes to determine how effects scaled along the quantitative invasion gradient.Furthermore,we collected growth cores of the studied native species,and we calculated aboveground biomass increments at the tree and stand levels.Then,we used generalized linear mixed-effects models to assess the impact of invasive species abundances on relative aboveground biomass increments of native tree species.We did not find a biologically or statistically significant impact of invasive R.pseudoacacia or P.serotina on the relative aboveground,biomass increments of native oaks and pines along the quantitative gradient of invader biomass or on the proportion of total stand biomass accounted for by invaders.The neophytes did not act as native tree growth stimulators but also did not compete with them for resources,which would escalate the negative impact of climate change on pines and oaks.The neophytes should not significantly modify the carbon sequestration capacity of the native species.Our work combines elements of the per capita effect of invasion with research on mixed forest management.
文摘In this paper,we prove some limsup results for increments and lag increments of G(t),which is a stable processe in random scenery.The proofs rely on the tail probability estimation of G(t).
基金supported by the National Natural Science Foundation of China(Nos.52272440,51875375)the China Postdoctoral Science Foundation Funded Project(No.2021M701503).
文摘As a data-driven approach, Deep Learning(DL)-based fault diagnosis methods need to collect the relatively comprehensive data on machine fault types to achieve satisfactory performance. A mechanical system may include multiple submachines in the real-world. During condition monitoring of a mechanical system, fault data are distributed in a continuous flow of constantly generated information and new faults will inevitably occur in unconsidered submachines, which are also called machine increments. Therefore, adequately collecting fault data in advance is difficult. Limited by the characteristics of DL, training existing models directly with new fault data of new submachines leads to catastrophic forgetting of old tasks, while the cost of collecting all known data to retrain the models is excessively high. DL-based fault diagnosis methods cannot learn continually and adaptively in dynamic environments. A new Continual Learning Fault Diagnosis method(CLFD) is proposed in this paper to solve a series of fault diagnosis tasks with machine increments. The stability–plasticity dilemma is an intrinsic issue in continual learning. The core of CLFD is the proposed Dual-branch Adaptive Aggregation Residual Network(DAARN).Two types of residual blocks are created in each block layer of DAARN: steady and dynamic blocks. The stability–plasticity dilemma is solved by assigning them with adaptive aggregation weights to balance stability and plasticity, and a bi-level optimization program is used to optimize adaptive aggregation weights and model parameters. In addition, a feature-level knowledge distillation loss function is proposed to further overcome catastrophic forgetting. CLFD is then applied to the fault diagnosis case with machine increments. Results demonstrate that CLFD outperforms other continual learning methods and has satisfactory robustness.
基金Supported by the Natural Science Foundation of Hubei Province of China(2011CDB229)
文摘In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen＇s law of iterated logarithm for a Wiener process.
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.
文摘Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.
文摘Let be a stable subordinator defined on a probability space and let at for t>0?be a non-negative valued function. In this paper, it is shown that under varying conditions on at, there exists a function such that where , , and .
基金Project Supported by National Science Fundation of China(1 9571 0 2 1 ) and Zhejiang Province
文摘Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.
文摘A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up and then experimentally verified.And the relation between depth increment and the minimum thickness tmin as well as its location was analyzed through the FEM model.Afterwards,the variation of depth increments was defined.The designed part was divided into three areas according to the main deformation mechanism,with Di(i=1,2) representing the two dividing locations.And three different values of depth increment,Δzi(i=1,2,3) were utilized for the three areas,respectively.Additionally,an orthogonal test was established to research the relation between the five process parameters(D and Δz) and tmin as well as its location.The result shows that Δz2 has the most significant influence on the thickness distribution for the corresponding area is the largest one.Finally,a single evaluating indicator,taking into account of both tmin and its location,was formatted with a linear weighted model.And the process parameters were optimized through a genetic algorithm integrated with an artificial neural network based on the evaluating index.The result shows that the proposed algorithm is satisfactory for the optimization of variable depth increment.
基金supported by National Forestry Public Welfare Foundation of China(201304205)National Science Foundation of China(31470578 and 31200363)+2 种基金Fujian Provincial Department of S&T Project(2016Y0083,2013YZ0001-1,2014J05044 and 2015Y0083)Xiamen Municipal Department of Science and Technology(3502Z20130037 and 3502Z20142016)Youth Innovation Promotion Association CAS
文摘Mid-subtropical forests are the main vegetation type of global terrestrial biomes, and are critical for maintaining the global carbon balance. However, estimates of forest biomass increment in mid-subtropical forests remain highly uncertain. It is critically important to determine the relative importance of different biotic and abiotic factors between plants and soil, particularly with respect to their influence on plant regrowth. Consequently,it is necessary to quantitatively characterize the dynamicspatiotemporal distribution of forest carbon sinks at a regional scale. This study used a large, long-term dataset in a boosted regression tree（BRT） model to determine the major components that quantitatively control forest biomass increments in a mid-subtropical forested region（Wuyishan National Nature Reserve, China）. Long-term,stand-level data were used to derive the forest biomass increment, with the BRT model being applied to quantify the relative contributions of various biotic and abiotic variables to forest biomass increment. Our data show that total biomass（t） increased from 4.62 9 106 to 5.30 9 106 t between 1988 and 2010, and that the mean biomass increased from 80.19 ± 0.39 t ha-1（mean ± standard error） to 94.33 ± 0.41 t ha-1in the study region. The major factors that controlled biomass（in decreasing order of importance） were the stand, topography, and soil. Stand density was initially the most important stand factor, while elevation was the most important topographic factor. Soil factors were important for forest biomass increment but have a much weaker influence compared to the other two controlling factors. These results provide baseline information about the practical utility of spatial interpolationmethods for mapping forest biomass increments at regional scales.
文摘A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.
文摘Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1 983
文摘In this paper,the models of increment distributions of stock price are constructed with two approaches. The first approach is based on limit theorems of random summation. The second approach is based on the statistical analysis of the increment distribution of the logarithms of stock prices.
文摘Context and background: A quantum formulation of vision in vertebrates was proposed in the early 1940s. The number of quanta useful for enabling vision was found. The time interval required for their absorption, however, was never specified. In the early 1950s, experimental data on the effects of light’s intensity increment on vision indicated that the quantum formulation is true only at low light’s intensities. In this case, a vaguely described signaling adaptation mechanism was invoked to explain the separation between vision at low and high intensities, accompanied by the switch from rod to cones as photoreceptors. Motivation: In this article, we want to prove the validity of the non-totally-quantum formulation and unveil the nature of the signaling adaptation mechanism. Hypothesis: To accomplish our proof, we hypothesize that the amount of energy transferred and conserved in light’s interaction with the eyes is given by the product of light’s intensity (or power) times its period. Method: We construct and use the plots of the trends of light’s intensity increments and the corresponding changes in the axon’s membrane capacitance versus adapting intensity. Results: We find that 1) the average solar light’s intensity is the critical value that separates low from high light’s intensity regimes in vision, and 2) changes in the capacitance of the axon’s membrane enable the signaling adaptation of vision when light’s intensity changes. Conclusions: We prove the validity of the non-totally-quantum formulation and unveil the nature of the signaling adaptation mechanism. Our proof is supported by the model based on light’s intensity times period as being the energy conserved in light-matter interaction This model suggests that 1) all the waves in the electromagnetic spectrum, at the correct intensity for each frequency, could be used to produce the effects of optogenetics in diagnostics and therapy, and 2) it takes seconds to minutes to see details in the dark when light is switched off.
文摘With the help of large deviation of Brownian motion in the Hölder norm,local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated.This paper promotes the corresponding results by Gantert and Wei.
基金partially supported by National Natural Science Foundation of China(12371150,12071003)Natural Science Foundation of Anhui Polytechnic University(2022AH050955,2022YQQ025,Xjky2022163)Zhejiang Province Philosophy and Social Science Planning Routine Subject(24NDJC131YB).
文摘Let X={X(t),t∈R+} be a centered space anisotropic Gaussian process values in R^(d) with non-stationary increments,whose components are independent but may not be identically distributed.Under certain conditions,then almost surely c_(1)≤ϕ-m(X([0,1]))≤c_(2),where ϕ denotes the exact Hausdorff measure associated with function ϕ(s)=s1/α_(k)+Σ_(i=1)k(1-αi/αk)log log 1/s for some 1≤k≤d,(α_(1),…,α_(d))∈(0,1]^(d).We also obtain the exact Hausdorff measure of the graph of X on[0,1].
基金Supported by National Natural Science Foundation of China(11661025)Science Research Foundation of Guangxi Education Department(YB2014117)+1 种基金Guangxi Natural Science Foundation(2018GXNSFBA281076,2017GXNSFBA198179)Guangxi Programme for Promoting Young Teachers’s Ability(2018KY0214).
文摘In this paper,we obtain the quasi sure local Chung’s functional law of the iterated logarithm for increments of a Brownian motion.As an application,a quasi sure Chung’s type functional modulus of continuity for a Brownian motion is also derived.
文摘A relationship was discovered between the amplification factor and the number of load increments that are needed to limit the relative error to one percent in second-order elastic analyses with a predictor-corrector solution scheme.Previous research by the authors proposed a design equation to determine the required minimum number of load increments based on an evaluation of the elastic critical buckling load ratio.Further research has shown that an approximate amplification factor equation that is based on the B2 multiplier equation produces similar results when the amplification factor is less than approximately four.Eleven moment frames are used to verify the use of the new approximate amplification factor in the proposed design equation.
文摘In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
