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数学进展 - 2018, Vol. 47(1): 129-138
研究论文
带形上随机游动的逃逸概率
Exit Probability of Random Walk on a Strip

张美娟
ZHANG Meijuan

中央财经大学统计与数学学院, 北京, 100081
School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, P. R. China

出版日期: 2018-01-25
2018, Vol. 47(1): 129-138
DOI: 10.11845/sxjz.2016071b


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摘要 逃逸概率是研究带形上随机游动极限性质的有力工具. 所谓逃逸概率, 是指游动在到达位置 $A$ 之前, 首次到达位置 $B$ 的概率. 关于逃逸概率的概率性质已得到深入研究. 本文对带形 $S= \mathbb{Z} \times\{1,2\}$ 上一类特殊的随机游动, 研究游动在到达 $-\infty$ 之前, 首次到达某位置的这类逃逸概率, 给出了逃逸概率矩阵的显式表达.
关键词 逃逸概率带形上的随机游动差分方程电网络全概率公式    
Abstract:Abstract:Exit probability is a useful tool in the study for random walk on a strip. The exit probability is a probability that a random walk first reaches the location $B$ before hitting the location $A$. Some probabilistic properties about exit probability have been revealed. In this paper, we consider a special random walk on a strip $S= \mathbb{Z} \times\{1,2\}$ and study such exit probability that a random walk reaches some location before hitting $-\infty$. We give the explicit expression for exit probability matrix.
Key wordsexit probability    random walk on a strip    difference equation    electric network    full probability formula
PACS:  O211.62  
基金资助:国家自然科学基金(No. 11601538), 中央财经大学2016年青年教师发展基金项目和中央财经大学学科建设经费.
通讯作者: E-mail: zhangmeijuan1227@163.com   
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