研究随机变量序列的部分和之和Tn=sum from i=1 to n(Si)(其中Sn=sum from i=1 to n(Xi))的极限性质,对强平稳NA序列,且EXi=0的条件下,获得了ETn2的稳定公式,并在此基础上,研究了其中心极限定理成立的条件,最后得到强平稳NA序列Tn的中...研究随机变量序列的部分和之和Tn=sum from i=1 to n(Si)(其中Sn=sum from i=1 to n(Xi))的极限性质,对强平稳NA序列,且EXi=0的条件下,获得了ETn2的稳定公式,并在此基础上,研究了其中心极限定理成立的条件,最后得到强平稳NA序列Tn的中心极限定理.展开更多
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
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
文摘研究随机变量序列的部分和之和Tn=sum from i=1 to n(Si)(其中Sn=sum from i=1 to n(Xi))的极限性质,对强平稳NA序列,且EXi=0的条件下,获得了ETn2的稳定公式,并在此基础上,研究了其中心极限定理成立的条件,最后得到强平稳NA序列Tn的中心极限定理.
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.
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
