JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (11): 119-126.doi: 10.6040/j.issn.1671-9352.0.2014.596

Previous Articles     Next Articles

A class of random walks in a random environment with singular jumps

FEI Shi-long1, BAI Yao-qian2   

  1. 1. School of Mathematics and Statistics, Suzhou University, Suzhou 234000, Anhui, China;
    2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • Received:2014-12-31 Revised:2015-07-22 Online:2015-11-20 Published:2015-12-09

PDF (PC)

700

Abstract: A class of random walks on half-line in a random environment with singular jumps were introduced, which promoted a case of random walks on half-line in a random environment with nearest-neighbor or bounded jumps. First of all, several sufficient and necessary conditions that recurrence and transience criteria of states were obtained by using suitable inequality and recurrence and transience criteria of Markov chains when the environment was fixed. Furthermore several criteria about positive recurrence and null recurrence of states were discussed assuming that the state was recurrent. At last assuming the environment is a sequences of random variables, the recurrence and transience criteria and criteria of positive recurrence and null recurrence were obtained by using the limit theory of random variables. These conclusions are the promotion of some results of other papers.

Key words: transience, positive recurrence, random walks, random environments, null recurrence, recurrence

CLC Number: 

  • O211.62
[1] SOLOMN F. Random walks in a random environment[J]. Ann Prob, 1975, 3(1):1-31.
[2] ALILI S. Asymptotic behavior for random walks in random environments[J]. J Appl Prob, 1999, 36(2):334-349.
[3] ZEITOUNI O. Random walks in random environment[C]//Lectures on probability theory and statistics. Berlin:Springer, 2004, 191-312.
[4] ANDJEL E. A zero or one law for one dimensional random walks in random environments[J]. Ann Prob, 1988, 16(2):722-729.
[5] ZHU Dongjin. The stationary distribution of markov chains in random environments[J].Chinese Journal of Applied Probability and Statistics, 2012, 28(4):337-344.
[6] ZHU Dongjin. The strong law of large numbers of random walk in random environments on half-line[J]. Chinese Journal of Applied Probability and Statistics, 2013, 29(1):97-105.
[7] KEY E S. Recurrence and transience criteria for random walk in a random environment[J]. Ann Prob, 1984, 12(2):529-560.
[8] BREMONT J. On some random walks on Z in random medium[J]. Ann Prob, 2002, 30(3):1266-1312.
[9] BREMONT J. One-dimensional finite range random walk in random medium and invariant measure equation[J]. Ann Inst H Poincar, 2009, 45(1):70-103.
[10] BI Qiuxiang. Some properties of RWIRE on half-line[J]. Chinese Journal of Applied Probability and Statistics, 1997, 13(2):120-124.
[11] 柳向东,戴永隆. 一类随机环境中半直线上的可逗留随机游动[J].数学物理学报, 2005, 25A(1):98-102. LIU Xiangdong, DAI Yonglong. A class of random walks on half-line in random environments[J]. Acta Mathematica Scientia, 2005, 25A(1):98-102.
[12] 胡学平,李会葆,徐耸.半直线上随机环境中随机游动的极限性质[J]. 应用概率统计, 2009, 25(6):611-617. HU Xueping, LI Huibao, XU Song. Limit properties for random walk in random environments on half-line[J]. Chinese Journal of Applied Probability and Statistics, 2009, 25(6):611-617.
[13] 费时龙. 随机环境中的成功游程[J]. 数学物理学报, 2013,33A(5):960-965. FEI Shilong. Success-runs in a random environment[J]. Acta Mathematica Scientia, 2013, 33A(5):960-965.
[14] Samuel Karlin, Howard M Taylor. A first course in stochastic processes[M]. New York:Academic Press, 1975.
[15] DURRETT R. Probability theory and examples[M]. New York:Duxbury Press, 2005.
[16] FELLER W. An introduction to probability theory and its applications[M]. New York:Wiley, 1968.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd