洪文明,张美娟.带形上随机环境中随机游动的内蕴分枝结构[J].数学年刊A辑,2016,37(4):405~420
带形上随机环境中随机游动的内蕴分枝结构
The Intrinsic Branching Structure for the Random Walk on a Strip in a Random Environment
Received: November 25, 2014  Revised: April 24, 2015
DOI:
中文关键词:  分枝结构, 带形上的随机游动, 随机环境, 击中时, 不变测度, 从粒子看环境
英文关键词:Branching structure, Random walk on a strip, Random environment, Hitting time, Invariant measure, Environments viewed from the particle
基金项目:本文受到国家自然科学基金 (No.11131003)和中央财经大学2016年青年教师发展基金的资助.
Author NameAffiliation
HONG Wenming School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China. 
ZHANG Meijuan School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China. 
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中文摘要:
      揭示了带形上随机环境中随机游动的内蕴分枝结构\!---\!带移民的多物种分枝过程. 利用内蕴分枝结构, 可精确表达游动的首次击中时. 给出了内蕴分枝结构的如下两个应用:\!\! (1) 计算出首次击中时的均值, 给出游动大数定律速度的显示表达,\!\!(2) 得到从粒子角度看环境的马氏链不变测度的密度函数的显示表达, 进而可用另一种``站在粒子看环境\!" 的方法直接证明游动的大数定律.
英文摘要:
      An intrinsic branching structure within the random walk on a strip in a random environment is revealed, which is a multi-type branching process with immigration. By the intrinsic branching structure, the authors give an explicit expression for the first hitting time. Two of its applications are obtained as follows. (1) Calculate the mean of the hitting time, and then give an explicit expression for the drift of the law of large numbers. (2) Use the branching structure to specify the density of the absolutely continuous invariant measure for the Markov chain of ``environments viewed from the particle". Then the law of large numbers are reproved by the method of ``the environment viewed from particles".
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