We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environmen...We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.展开更多
Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD）...Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD） random variables are also obtained, which extend and improve the related known works in the literature.展开更多
The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the ...The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).展开更多
For a sequence of arbitrarily dependent m-valued random variables （Xn） n∈N , the generalized strong limit theorem of the delayed average is investigated. In our proof, we improved the method proposed by Liu [6] . A...For a sequence of arbitrarily dependent m-valued random variables （Xn） n∈N , the generalized strong limit theorem of the delayed average is investigated. In our proof, we improved the method proposed by Liu [6] . As an application, we also studied some limit properties of delayed average for inhomogeneous Markov chains.展开更多
In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented...In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.展开更多
We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles,focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles.For the...We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles,focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles.For the central limit theorem of β-Laguerre ensembles,we follow the idea in[1]while giving a modified version for the generalized case.Then we use the total variation distance between the two sorts of ensembles to obtain the limiting behavior of β-Jacobi ensembles.展开更多
First,a class of strong limit theorems are proved by constructing two nonnegative martingales.Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the pape...First,a class of strong limit theorems are proved by constructing two nonnegative martingales.Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the paper.Finally,some strong limit theorems for the even-odd Markov chain fields and Markov chain fields are obtained.展开更多
The periodically forced 2D Navier-Stokes equation with a degenerate noise is studied.For the Markov chain obtained by restricting the solution process to the Poincarésection,we prove a quantitative version of the...The periodically forced 2D Navier-Stokes equation with a degenerate noise is studied.For the Markov chain obtained by restricting the solution process to the Poincarésection,we prove a quantitative version of the strong law of large numbers and the central limit theorem with explicit convergence rates.A law of the iterated logarithm is also obtained.The proof is based on a martingale approximation procedure.展开更多
In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail p...In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail probability of the life period of W is studied.Based on above results,two conditional limit theorems for W are established.展开更多
In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit th...In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit theorem for independent random vectors is established,the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found,and a Lévy’s characterization of a multi-dimensional G-Brownian motion is obtained.展开更多
Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit t...Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.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
In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of...In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.展开更多
We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate t...We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N＋ and Tn展开更多
Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normaliz...Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normalized population size W_n converges almost surely to a finite random variable W. Secondly, we show criterions for the non-degeneracy and for the existence of moments of the limit random variable W. Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n.展开更多
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem ...The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.展开更多
In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.
We obtain sufficient criteria for central limit theorems （CLTs） for ergodic continuous-time Markov chains （CTMCs）. We apply the results to establish CLTs for continuous-time single birth processes. Moreover, we pr...We obtain sufficient criteria for central limit theorems （CLTs） for ergodic continuous-time Markov chains （CTMCs）. We apply the results to establish CLTs for continuous-time single birth processes. Moreover, we present an explicit expression of the time average variance constant for a single birth process whenever a CLT exists. Several examples are given to illustrate these results.展开更多
In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.
基金partially supported by the National Natural Science Foundation of China(NSFC,11101039,11171044,11271045)a cooperation program between NSFC and CNRS of France(11311130103)+1 种基金the Fundamental Research Funds for the Central UniversitiesHunan Provincial Natural Science Foundation of China(11JJ2001)
文摘We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.
基金Supported by the National Natural Science Foundation of China (Grant No.11271161)
文摘Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD） random variables are also obtained, which extend and improve the related known works in the literature.
基金the National Natural Science Foundation of China!(No.19361060)and the Mathematical Center of the State Education Commission of
文摘The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).
基金Supported by the National Natural Science Foundation of China (10871200)
文摘In this article, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d, random environments.
基金Supported by the National Natural Science Foundation of China (11071104, 11226210)the Foundation of Anhui Education Committee (KJ2012B117)+1 种基金Anhui University of Technolog Graduate Innovation Fund (D2011025)Research Foundation for Advanced Talents of Jiangsu University(11JDG116)
文摘For a sequence of arbitrarily dependent m-valued random variables （Xn） n∈N , the generalized strong limit theorem of the delayed average is investigated. In our proof, we improved the method proposed by Liu [6] . As an application, we also studied some limit properties of delayed average for inhomogeneous Markov chains.
基金Supported by the National Nature Science Foundation of China (Grant No. 11101014)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20101103120016)+4 种基金the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No. PHR20110822)Training Programme Foundation for the Beijing Municipal Excellent Talents (Grant No. 2010D005015000002)the Fundamental Research Foundation of Beijing University of Technology (Grant No. X4006013201101)Education Department Science Project of Hebei Province (Grant No. Z2010297)Science Project of Shijiazhuang University of Economics (Grant No. XN0912)
文摘In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.
文摘We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles,focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles.For the central limit theorem of β-Laguerre ensembles,we follow the idea in[1]while giving a modified version for the generalized case.Then we use the total variation distance between the two sorts of ensembles to obtain the limiting behavior of β-Jacobi ensembles.
基金Supported by the Special Fundation of Tianjin Education Committee(2006ZH91)Supported by the Key Discipline of Applied Mathematics at Tianjin University of Commerce(X0803)
文摘First,a class of strong limit theorems are proved by constructing two nonnegative martingales.Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the paper.Finally,some strong limit theorems for the even-odd Markov chain fields and Markov chain fields are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.12090010 and 12090013)。
文摘The periodically forced 2D Navier-Stokes equation with a degenerate noise is studied.For the Markov chain obtained by restricting the solution process to the Poincarésection,we prove a quantitative version of the strong law of large numbers and the central limit theorem with explicit convergence rates.A law of the iterated logarithm is also obtained.The proof is based on a martingale approximation procedure.
基金supported by China Postdoctoral Science Foundation(Grant No.2020M680269)National Natural Science Foundation of China(Grant No.12101023)+1 种基金the second author is supported by National Natural Science Foundation of China(Grant No.11871103)the National Key Research and Development Program of China(Grant No.2020YFA0712900)。
文摘In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail probability of the life period of W is studied.Based on above results,two conditional limit theorems for W are established.
基金Supported by grants from the NSF of China(Grant No.11731012,12031005)Ten Thousands Talents Plan of Zhejiang Province(Grant No.2018R52042)+1 种基金NSF of Zhejiang Province(Grant No.LZ21A010002)the Fundamental Research Funds for the Central Universities.
文摘In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit theorem for independent random vectors is established,the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found,and a Lévy’s characterization of a multi-dimensional G-Brownian motion is obtained.
基金Supported by Shandong Provincial Natural Science Foundation(Grant No.ZR2021MA085)National Natural Science Foundation of China(Grant No.11971063)。
文摘Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.
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
文摘In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.
文摘We consider linear Hawkes process Nt and its inverse process Tn. The limit theorems for Nt are well known and studied by many authors. In this paper, we study the limit theorems for Tn. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for Tn. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N＋ and Tn
基金supported by National Natural Science Foundation of China (Grants Nos. 11401590 and 11571052)
文摘Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normalized population size W_n converges almost surely to a finite random variable W. Secondly, we show criterions for the non-degeneracy and for the existence of moments of the limit random variable W. Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n.
基金supported by National Natural Science Foundation of China(Grant No.11731012)the Fundamental Research Funds for the Central Universities+1 种基金the State Key Development Program for Basic Research of China(Grant No.2015CB352302)Zhejiang Provincial Natural Science Foundation(Grant No.LY17A010016)。
文摘The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.
基金Supported by NNSFC(Grant No.11371191)Jiangsu Province Basic Research Program(Natural Science Foundation)(Grant No.BK2012720)
文摘In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.
文摘We obtain sufficient criteria for central limit theorems （CLTs） for ergodic continuous-time Markov chains （CTMCs）. We apply the results to establish CLTs for continuous-time single birth processes. Moreover, we present an explicit expression of the time average variance constant for a single birth process whenever a CLT exists. Several examples are given to illustrate these results.
基金1)This work is supported by NSFC(10571159),SRFDP(2002335090)and KRF(D00008)2)This work is supported by NSFC(10401037)and China Postdoctoral Science Foundation3)This work is supported by the Brain Korea 21 Project in 2005
文摘In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.
