Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN result...Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN results(of Dvoretzky-Erdos'type).Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1+γThey also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distributions with constant exponent 2.This exponent is obviously independent of the parameterγ∈(0,1),which is a surprise to us at first sight.展开更多
Let {X, X i ; i≥1} be a sequence of i.i.d.r.v’.s, Z (t)= t i=1 X i,t≥0. Consider the renewal process N(t) =inf{x; Z(x) 】t}. In this paper we study the necessary momentconditions for { N(t) ...Let {X, X i ; i≥1} be a sequence of i.i.d.r.v’.s, Z (t)= t i=1 X i,t≥0. Consider the renewal process N(t) =inf{x; Z(x) 】t}. In this paper we study the necessary momentconditions for { N(t) ; t≥0} approximating to Wiener processes.Our results have improved those of Csrg, Horváth and Stei, Horváth and Steinebach展开更多
The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To prov...The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.展开更多
Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be depende...Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.展开更多
This paper extends the ordinary renewal risk model to the case where the premium income process,based on a renewal counting process,is no longer a linear function;and the total claim amount process is described by a c...This paper extends the ordinary renewal risk model to the case where the premium income process,based on a renewal counting process,is no longer a linear function;and the total claim amount process is described by a compound renewal process.For this realistic risk model,the large deviations for the claim surplus process is investigated.展开更多
In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected proces...In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.展开更多
The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary rene...The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.展开更多
Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to...Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.展开更多
The feasibility analysis of projects for the preservation of the historical heritage buildings is an important problem concerning the evaluation of ＂the total cost of intervention＂, which includes all the future dam...The feasibility analysis of projects for the preservation of the historical heritage buildings is an important problem concerning the evaluation of ＂the total cost of intervention＂, which includes all the future damage costs. The total cost of intervention represents a suitable measure of the expected deterioration risk and its evolution obviously depends on the damage process which buildings are subjected to. That damage phenomena affecting masonry buildings pleased into an aggressive environment are suitably modelled by renewal processes： this happens both in the case of catastrophic events, or in the case of the so-called ＂natural aging＂, in which damage comes off gradually in time. In the hypothesis ofa Markovian renewal process （Mrp） describing the damage process, the total cost of all the future damage is evaluated taking into account both the damage aspects： damages due to catastrophic aspects and damages due to aggressive environment, supposing different maintenance and/or rehabilitation scenarios. A semi-Markov process （s-Mp） is defined to model the damage rehabilitation history of buildings in presence of seismic events, natural ageing and rehabilitation strategies. The expected rewards connected to the process are defined; they represent a significant measure of the risk.展开更多
This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and F...This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.展开更多
This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk m...This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.展开更多
The paper presents a successful design and good result of grid voltage feed-forward control strategy with no damping regulator of LCL filter applied in Three-phase Pulse Width Modulation( PWM) rectifier under unbalanc...The paper presents a successful design and good result of grid voltage feed-forward control strategy with no damping regulator of LCL filter applied in Three-phase Pulse Width Modulation( PWM) rectifier under unbalance grid condition for renewable energy processing. It is demonstrated that the closed-loop current control is decoupled with the grid voltage feed-forward control,and good waveform of grid current with low order harmonics is obtained under unbalance grid condition. This novel strategy is simple and reliable,applied with PI regulator but no resonant controller in α,β two-phase stationary frame. Moreover,the results of experiment and simulation are also illustrated to validate the novel strategy well applied in the closed-loop current control system under unbalanced grid condition.展开更多
In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and consta...In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.展开更多
Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a^(i-1)X_i,i=1,2,...} forms a renewal process.In thispaper,the GP is used to ana...Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a^(i-1)X_i,i=1,2,...} forms a renewal process.In thispaper,the GP is used to analyze the data from a series of events.A nonparametric method is introduced forthe estimation of the three parameters in the GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.展开更多
Reliability-redundancy allocation,preventive maintenance,and spare parts logistics are crucial for achieving system reliability and availability goal.Existing methods often concentrate on specific scopes of the system...Reliability-redundancy allocation,preventive maintenance,and spare parts logistics are crucial for achieving system reliability and availability goal.Existing methods often concentrate on specific scopes of the system’s lifetime.This paper proposes a joint redundancymaintenance-inventory allocation model that simultaneously optimizes redundant component,replacement time,spares stocking,and repair capacity.Under reliability and availability criteria,our objective is to minimize the system’s lifetime cost,including design,manufacturing,and operational phases.We develop a unified system availability model based on ten performance drivers,serving as the foundation for the establishment of the lifetimebased resource allocation model.Superimposed renewal theory is employed to estimate spare part demand from proactive and corrective replacements.A bisection algorithm,enhanced by neighborhood exploration,solves the complex mixed-integer,nonlinear optimization problem.The numerical experiments show that component redundancy is preferred and necessary if one of the following situations occurs:extremely high system availability is required,the fleet size is small,the system reliability is immature,the inventory holding is too costly,or the handson replacement time is prolonged.The joint allocation model also reveals that there exists no monotonic relation between spares stocking level and system availability.展开更多
In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the as...In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.展开更多
In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common h...In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.展开更多
基金This work was supported by the National Natural Science Foundation of China(Nos.11871162,11771286,11271255,11271077,11001173,11790273)the Key Laboratory of Mathematics for Non linear Science,Fudan University.
文摘Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN results(of Dvoretzky-Erdos'type).Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1+γThey also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distributions with constant exponent 2.This exponent is obviously independent of the parameterγ∈(0,1),which is a surprise to us at first sight.
文摘Let {X, X i ; i≥1} be a sequence of i.i.d.r.v’.s, Z (t)= t i=1 X i,t≥0. Consider the renewal process N(t) =inf{x; Z(x) 】t}. In this paper we study the necessary momentconditions for { N(t) ; t≥0} approximating to Wiener processes.Our results have improved those of Csrg, Horváth and Stei, Horváth and Steinebach
文摘The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.
基金Supported by the National Natural Science Foundation of China(Nos.11571058&11301481)Humanities and Social Science Foundation of the Ministry of Education of China(No.17YJC910007)+1 种基金Zhejiang Provincial Natural Science Foundation of China(No.LY17A010004)Fundamental Research Funds for the Central Universities(No.DUT17LK31)
文摘Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.
基金Supported by Anhui Provincial Colleges and Universities Teaching and Research Projects(2008jyxm556)
文摘This paper extends the ordinary renewal risk model to the case where the premium income process,based on a renewal counting process,is no longer a linear function;and the total claim amount process is described by a compound renewal process.For this realistic risk model,the large deviations for the claim surplus process is investigated.
文摘In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.
基金The National Natural Science Foundation of China (No.10671139,11001052)the Natural Science Foundation of Jiangsu Province(No. BK2008284 )+2 种基金China Postdoctoral Science Foundation ( No.20100471365)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province (No. 09KJD110003)Postdoctoral Research Program of Jiangsu Province (No.0901029C)
文摘The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.
文摘Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.
文摘The feasibility analysis of projects for the preservation of the historical heritage buildings is an important problem concerning the evaluation of ＂the total cost of intervention＂, which includes all the future damage costs. The total cost of intervention represents a suitable measure of the expected deterioration risk and its evolution obviously depends on the damage process which buildings are subjected to. That damage phenomena affecting masonry buildings pleased into an aggressive environment are suitably modelled by renewal processes： this happens both in the case of catastrophic events, or in the case of the so-called ＂natural aging＂, in which damage comes off gradually in time. In the hypothesis ofa Markovian renewal process （Mrp） describing the damage process, the total cost of all the future damage is evaluated taking into account both the damage aspects： damages due to catastrophic aspects and damages due to aggressive environment, supposing different maintenance and/or rehabilitation scenarios. A semi-Markov process （s-Mp） is defined to model the damage rehabilitation history of buildings in presence of seismic events, natural ageing and rehabilitation strategies. The expected rewards connected to the process are defined; they represent a significant measure of the risk.
基金Supported by the Natural Science Foundation of the Education Department of Anhui Province(0505101)
文摘This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.
基金Supported by the Natural Science Foundation of Hunan (No. 08JJ3004)
文摘This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.
文摘The paper presents a successful design and good result of grid voltage feed-forward control strategy with no damping regulator of LCL filter applied in Three-phase Pulse Width Modulation( PWM) rectifier under unbalance grid condition for renewable energy processing. It is demonstrated that the closed-loop current control is decoupled with the grid voltage feed-forward control,and good waveform of grid current with low order harmonics is obtained under unbalance grid condition. This novel strategy is simple and reliable,applied with PI regulator but no resonant controller in α,β two-phase stationary frame. Moreover,the results of experiment and simulation are also illustrated to validate the novel strategy well applied in the closed-loop current control system under unbalanced grid condition.
基金Supported by National Natural Science Foundation of China (Grant No. 10871177)Specialized Research Fund for Doctor Program of Higher Education (Grant No. 20060335032)
文摘In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.
文摘Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a^(i-1)X_i,i=1,2,...} forms a renewal process.In thispaper,the GP is used to analyze the data from a series of events.A nonparametric method is introduced forthe estimation of the three parameters in the GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.
基金supported by the US National Science Foundation(Grant No.1704933)The research of the second and the third authors are supported by the National Natural Science Foundation of China(Grant No.72231008)the Natural Science Basic Research Program of Shaanxi(Program No.2022JQ734).
文摘Reliability-redundancy allocation,preventive maintenance,and spare parts logistics are crucial for achieving system reliability and availability goal.Existing methods often concentrate on specific scopes of the system’s lifetime.This paper proposes a joint redundancymaintenance-inventory allocation model that simultaneously optimizes redundant component,replacement time,spares stocking,and repair capacity.Under reliability and availability criteria,our objective is to minimize the system’s lifetime cost,including design,manufacturing,and operational phases.We develop a unified system availability model based on ten performance drivers,serving as the foundation for the establishment of the lifetimebased resource allocation model.Superimposed renewal theory is employed to estimate spare part demand from proactive and corrective replacements.A bisection algorithm,enhanced by neighborhood exploration,solves the complex mixed-integer,nonlinear optimization problem.The numerical experiments show that component redundancy is preferred and necessary if one of the following situations occurs:extremely high system availability is required,the fleet size is small,the system reliability is immature,the inventory holding is too costly,or the handson replacement time is prolonged.The joint allocation model also reveals that there exists no monotonic relation between spares stocking level and system availability.
基金supported by the National Natural Science Foundation of China under Grant No.11471053
文摘In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081) .
文摘In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.
