M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large devi...M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.展开更多
In this work, the sample path large deviations for independent, identically distributed random variables under sub-linear expectations are established. The results obtained in sublinear expectation spaces extend the c...In this work, the sample path large deviations for independent, identically distributed random variables under sub-linear expectations are established. The results obtained in sublinear expectation spaces extend the corresponding ones in probability space.展开更多
The adaptive filtering algorithm with a fixed projection order is unable to adjust its performance in response to changes in the external environment of airborne radars.To overcome this limitation,a new approach is in...The adaptive filtering algorithm with a fixed projection order is unable to adjust its performance in response to changes in the external environment of airborne radars.To overcome this limitation,a new approach is introduced,which is the variable projection order Ekblom norm-promoted adaptive algorithm(VPO-EPAA).The method begins by examining the mean squared deviation(MSD)of the EPAA,deriving a formula for its MSD.Next,it compares the MSD of EPAA at two different projection orders and selects the one that minimizes the MSD as the parameter for the current iteration.Furthermore,the algorithm’s computational complexity is analyzed theoretically.Simulation results from system identification and self-interference cancellation show that the proposed algorithm performs exceptionally well in airborne radar signal self-interference cancellation,even under various noise intensities and types of interference.展开更多
In this paper,we consider a class of dependent Bernoulli variables,which has the following form:for k≥m,P(Xk+1=1jFk)=Σm i=1θiXk+1i+θ0p,where m is a positive integer,Σmi=0θi=1,Fn=σ{X1,……,Xn},0<p<1.The co...In this paper,we consider a class of dependent Bernoulli variables,which has the following form:for k≥m,P(Xk+1=1jFk)=Σm i=1θiXk+1i+θ0p,where m is a positive integer,Σmi=0θi=1,Fn=σ{X1,……,Xn},0<p<1.The convergence rate of the strong law of large numbers and the moderate deviation principle for the model are established.Furthermore,we study some properties of parameter estimation for the model.展开更多
The purpose of this paper is to broaden the knowledge of mean difference and,<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="fon...The purpose of this paper is to broaden the knowledge of mean difference and,<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">in particular, of an important distribution model known as Tukey lambda, which is generally used to choose a model to fit data.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">We have obtained compact formulas, which are not yet reported in literature, of mean deviation and mean difference related to the said distribution model.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">These results made it possible to analyze the relationships among variability indexes, namely standard deviation, mean deviation and mean difference, regarding Tukey lambda model.展开更多
Compared to terrestrial plants whose diversity is more directly influenced by climate,aquatic plant diversity is considered to be more dependent on water environments.Therefore,it could be predicted that the phylogene...Compared to terrestrial plants whose diversity is more directly influenced by climate,aquatic plant diversity is considered to be more dependent on water environments.Therefore,it could be predicted that the phylogenetic relatedness of terrestrial plants is more susceptible to climate filtering than that of aquatic plants.We compiled a comprehensive distribution dataset of herbaceous angiosperms in China,including both terrestrial and aquatic species.We compared the phylogenetic relatedness and its environmental correlation of the two groups,using the standardized effect size of phylogenetic diversity(PD_(ses))and the standardized effect size of mean phylogenetic distance(MPD_(ses)),which reflect shallow and deep evolutionary histories,respectively.We also use the deviation of PD_(ses)(ΔPD_(ses))and MPD_(ses)(ΔMPD_(ses))between terrestrial and aquatic plants to reflect differences in the phylogenetic relatedness between terrestrial and aquatic plants.Our results showed that the geographical patterns of PD_(ses)and MPD_(ses)between aquatic and terrestrial plants are roughly consistent.ΔPD_(ses)andΔMPD_(ses)between terrestrial and aquatic plants vary across the geographical scale and environmental gradient.Environmental variables(current climate,historical climate change and topography)explained more of the variation in PD_(ses)and MPD_(ses)of terrestrial plants than that of aquatic plants,with the current climate explaining more ofΔPD_(ses)andΔMPD_(ses)between terrestrial and aquatic plants.Our results reveal the differential impacts of large-scale environmental factors on the phylogenetic relatedness of terrestrial versus aquatic plant communities,providing a new perspective for understanding the ecological and evolutionary dynamics of these two distinct plant assemblages.展开更多
Using the theroy of topological degree, the paper studies the periodic solutions to a type of neutral Liénard equation with state-dependent deviation variable. A sufficient condition for the existence of periodic...Using the theroy of topological degree, the paper studies the periodic solutions to a type of neutral Liénard equation with state-dependent deviation variable. A sufficient condition for the existence of periodic solution is obtained.展开更多
We obtain sufficient conditions for class of second order neutral functional theorem of the coincidence degree. the existence of periodic solution to a differential equation, using continuation
We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certai...We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand(1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram′er(1938),Bahadur-Rao(1960) and Sakhanenko(1991). We also show that our bound can be used to improve a recent inequality of Pinelis(2014).展开更多
We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko...We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.展开更多
Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of pa...Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.展开更多
Let{X,X_(n);n≥1}be a sequence of i.i.d.non-degenerate real-valued random variables with EX^(2)<∞.Let S_(n)=∑_(i=1)^(n)X_(i),n≥1.Let g(·):[0,∞)→[0,∞)be a nondecreasing regularly varying function with in...Let{X,X_(n);n≥1}be a sequence of i.i.d.non-degenerate real-valued random variables with EX^(2)<∞.Let S_(n)=∑_(i=1)^(n)X_(i),n≥1.Let g(·):[0,∞)→[0,∞)be a nondecreasing regularly varying function with indexρ≥0 and limt→∞g(t)=∞.Letμ=EX andσ^(2)=E(X−μ)^(2).In this paper,on the scale g(log n),we obtain precise asymptotic estimates for the probabilities of moderate deviations of the form log P(S_(n)−nμ>x√ng(log n)),log P(S_(n)−nμ<−x√ng(log n)),and log P(|S_(n)−nμ|>x√ng(log n))for all x>0.Unlike those known results in the literature,the moderate deviation results established in this paper depend on both the variance and the asymptotic behavior of the tail distribution of X.展开更多
基金Partly supported by the National Natural Science Foundation of China and the Ministry of Education of ChinaPartly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,Jiaghan University
文摘M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.
基金Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University (Grant No. 102/01003002031)Academic Achievement Re-cultivation Project of Jingdezhen Ceramic University (Grant No. 215/205062777)the Science and Technology Research Project of Jiangxi Provincial Department of Education of China (Grant No. GJJ2201041)。
文摘In this work, the sample path large deviations for independent, identically distributed random variables under sub-linear expectations are established. The results obtained in sublinear expectation spaces extend the corresponding ones in probability space.
基金supported by the Shan⁃dong Provincial Natural Science Foundation(No.ZR2022MF314).
文摘The adaptive filtering algorithm with a fixed projection order is unable to adjust its performance in response to changes in the external environment of airborne radars.To overcome this limitation,a new approach is introduced,which is the variable projection order Ekblom norm-promoted adaptive algorithm(VPO-EPAA).The method begins by examining the mean squared deviation(MSD)of the EPAA,deriving a formula for its MSD.Next,it compares the MSD of EPAA at two different projection orders and selects the one that minimizes the MSD as the parameter for the current iteration.Furthermore,the algorithm’s computational complexity is analyzed theoretically.Simulation results from system identification and self-interference cancellation show that the proposed algorithm performs exceptionally well in airborne radar signal self-interference cancellation,even under various noise intensities and types of interference.
文摘In this paper,we consider a class of dependent Bernoulli variables,which has the following form:for k≥m,P(Xk+1=1jFk)=Σm i=1θiXk+1i+θ0p,where m is a positive integer,Σmi=0θi=1,Fn=σ{X1,……,Xn},0<p<1.The convergence rate of the strong law of large numbers and the moderate deviation principle for the model are established.Furthermore,we study some properties of parameter estimation for the model.
文摘The purpose of this paper is to broaden the knowledge of mean difference and,<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">in particular, of an important distribution model known as Tukey lambda, which is generally used to choose a model to fit data.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">We have obtained compact formulas, which are not yet reported in literature, of mean deviation and mean difference related to the said distribution model.<span style="font-family:;" "=""> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">These results made it possible to analyze the relationships among variability indexes, namely standard deviation, mean deviation and mean difference, regarding Tukey lambda model.
基金National Science Foundation of China(32260046)Thousand Talents Program of Jiangxi Province(jxsq2023101079).
文摘Compared to terrestrial plants whose diversity is more directly influenced by climate,aquatic plant diversity is considered to be more dependent on water environments.Therefore,it could be predicted that the phylogenetic relatedness of terrestrial plants is more susceptible to climate filtering than that of aquatic plants.We compiled a comprehensive distribution dataset of herbaceous angiosperms in China,including both terrestrial and aquatic species.We compared the phylogenetic relatedness and its environmental correlation of the two groups,using the standardized effect size of phylogenetic diversity(PD_(ses))and the standardized effect size of mean phylogenetic distance(MPD_(ses)),which reflect shallow and deep evolutionary histories,respectively.We also use the deviation of PD_(ses)(ΔPD_(ses))and MPD_(ses)(ΔMPD_(ses))between terrestrial and aquatic plants to reflect differences in the phylogenetic relatedness between terrestrial and aquatic plants.Our results showed that the geographical patterns of PD_(ses)and MPD_(ses)between aquatic and terrestrial plants are roughly consistent.ΔPD_(ses)andΔMPD_(ses)between terrestrial and aquatic plants vary across the geographical scale and environmental gradient.Environmental variables(current climate,historical climate change and topography)explained more of the variation in PD_(ses)and MPD_(ses)of terrestrial plants than that of aquatic plants,with the current climate explaining more ofΔPD_(ses)andΔMPD_(ses)between terrestrial and aquatic plants.Our results reveal the differential impacts of large-scale environmental factors on the phylogenetic relatedness of terrestrial versus aquatic plant communities,providing a new perspective for understanding the ecological and evolutionary dynamics of these two distinct plant assemblages.
基金Supported by the Education Department of Shanghai and the Youth Projecet Foundation of USST.
文摘Using the theroy of topological degree, the paper studies the periodic solutions to a type of neutral Liénard equation with state-dependent deviation variable. A sufficient condition for the existence of periodic solution is obtained.
基金Supported by the Education Department of Anhui Natural Science Foundation (2004kj0282006KJ245B).
文摘We obtain sufficient conditions for class of second order neutral functional theorem of the coincidence degree. the existence of periodic solution to a differential equation, using continuation
基金supported by the Post-Graduate Study Abroad Program sponsored by China Scholarship CouncilNational Natural Science Foundation of China(Grant Nos.11171044 and11401590)
文摘We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand(1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram′er(1938),Bahadur-Rao(1960) and Sakhanenko(1991). We also show that our bound can be used to improve a recent inequality of Pinelis(2014).
基金supported by National Natural Science Foundation of China (Grant Nos. 11601375 and 11626250)
文摘We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.
基金supported by National Natural Science Foundation of China (Grant No.11001077)
文摘Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.
基金Supported by Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2019-06065)National Natural Science Foundation of China(Grant No.NSFC-11971154)。
文摘Let{X,X_(n);n≥1}be a sequence of i.i.d.non-degenerate real-valued random variables with EX^(2)<∞.Let S_(n)=∑_(i=1)^(n)X_(i),n≥1.Let g(·):[0,∞)→[0,∞)be a nondecreasing regularly varying function with indexρ≥0 and limt→∞g(t)=∞.Letμ=EX andσ^(2)=E(X−μ)^(2).In this paper,on the scale g(log n),we obtain precise asymptotic estimates for the probabilities of moderate deviations of the form log P(S_(n)−nμ>x√ng(log n)),log P(S_(n)−nμ<−x√ng(log n)),and log P(|S_(n)−nμ|>x√ng(log n))for all x>0.Unlike those known results in the literature,the moderate deviation results established in this paper depend on both the variance and the asymptotic behavior of the tail distribution of X.
