北京大学期刊网　|　作者　　审稿人　　编委专家　　工作人员 首页　  |  　关于　  |  　浏览　  |  　投稿指南　  |  　新闻公告
 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
 PDF [418 KB] 202 下载 315 浏览 引用导出
0
/   /   推荐

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

 [1] Bolthausen, E. and Goldsheid, I., Recurrence and transience of random walks in random environments on a strip, Comm. Math. Phys., 2000, 214(2): 429-447.[2] Brémont, J., On some random walks on $\mathbb{Z}$ in random medium, Ann. Probab., 2002, 30(3): 1266-1312.[3] Doyle, P.G. and Snell, J.L., Random Walks and Electric Networks, Carus Math. Monogr., No. 22, Washington, DC: Math. Assoc. Amer., 2000.[4] Goldsheid, I., Linear and sub-linear growth and the CLT for hitting times of a random walk in random environments on a strip, Probab. Theory Related Fields, 2008, 141(3): 471-511.[5] Hong, W.M. and Wang, H.M.,Intrinsic branching structure within $(L-1)$ random walk in random environment and its applications, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2013, 16(1): 1350006, 14 pages.[6] Hong, W.M. and Zhang, L., Branching structure for the transient $(1, R)$-random walk in random environment and its applications, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2010, 13(4): 589-618.[7] Hong, W.M. and Zhang, M.J., Branching structure for the transient random walk in a random environment on a strip and its application, Chinese Ann. Math. Ser. A, 2016, 37(4): 405-420 (in Chinese).[8] Hong, W.M., Zhang, M.J. and Zhao, Y.Q., Light-tailed behavior of stationary distribution for state-dependent random walks on a strip, Front. Math. China, 2014, 9(4): 813-834.[9] Roitershtein, A., Transient random walks on a strip in a random environment, Ann. Probab., 2008, 36(6): 2354-2387.[10] Zeitouni, O., Random walks in random environment, In: Lectures on Probability Theory and Statistics (Picard, J. ed.), Lecture Notes in Math., Vol. 1837, Berlin: Springer-Verlag: 2004, 189-312.[11] Zhang, M.J., Large deviations for hitting times of a random walk in random environment on a strip, Acta Math. Sin., Engl. Ser., 2014, 30(3): 395-410.
 [1] 邱玲,胡雪萍. 关于线性差分方程的超越亚纯解的性质的结论[J]. 数学进展, 2017, 46(5): 743-754. [2] 刘树堂,张炳根. 泛函偏差分方程定性理论的发展[J]. 数学进展, 2003, 32(4): 385-397.
Viewed
Full text

Abstract

Cited

Discussed