广义耦合随机徘徊过程的存在性  

Existence of generalized coupled random walk

作　　者：郑晓阳[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2006年第4期621-624,共4页Journal of Harbin Engineering University

基　　金：哈尔滨工程大学基础研究基金资助项目(HEUF04022)

摘　　要：耦合随机徘徊过程的直观描述为:在每个u∈S处,有一个指数钟,这些指数钟相互独立,服从参数为1的Poisson分布.当在u处的指数钟响时,位于u处的粒子独立地以概率p(u,v)转移到v处.近年来耦合随机徘徊过程得到国际上概率论学者的广泛研究,但仅限于每次转移一个粒子的情形.文中使用的主要方法为从有限位置集到无限位置集的过渡和随机过程的耦合.对上述模型进行了推广,讨论了位置集为可列集且每次转移多个粒子的情形,并证明了广义耦合随机徘徊过程的存在性.可得当位置集为可列集且每次转移多个粒子时,耦合随机徘徊过程是存在的且为一无穷质点马氏过程.The intuitive description of coupled random walk processes is that at each μ∈ S there is an exponential clock. These exponential clocks using a Poisson distribution with one parameter are independent of each other. When the exponential clock at μ∈ S is stroked, a particle moves from μ to ν independently. In recent years this type of process has been widely studied by probability experts. However, previous re search involved a situation in which at each point in time there is one particle that moves from one site to another. The model was improved and the existence of a generalized coupled random walk was proven. The main result is that as S is an infinite sequence set and when several particles move from one set to another at each time, an interacting particle system exists. The main methods to achieve this is the transition from a finite set to infinite set and the coupling of stochastic processes.

关 键 词：耦合随机徘徊过程 耦合 存在性 

分 类 号：O211.6[理学—概率论与数理统计]