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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (11): 119-126.doi: 10.6040/j.issn.1671-9352.0.2014.596

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一类具有奇异跳动的随机环境中的随机游动

费时龙1, 柏跃迁2   

  1. 1. 宿州学院数学与统计学院, 安徽 宿州 234000;
    2. 北京师范大学数学科学学院, 北京 100875
  • 收稿日期:2014-12-31 修回日期:2015-07-22 出版日期:2015-11-20 发布日期:2015-12-09
  • 作者简介:费时龙(1980-),男,硕士,讲师,研究方向为随机过程的研究.E-mail:fsl627@sina.com
  • 基金资助:
    国家自然科学基金资助项目(10901003);安徽省高等学校省级自然科学基金资助项目(KJ2013B288);安徽省创新训练项目(AH201410379079);宿州学院安徽省煤矿勘探工程技术研究中心开放课题资助项目(2013YKF04)

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

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摘要： 引入了一类具有奇异跳动的半直线上随机环境中的随机游动模型,该模型是对半直线上一维紧邻或有界跳幅的随机环境中随机游动模型的推广。利用经典马氏链的常返、暂留准则并结合适当的不等式构造出在固定环境情形下状态的常返、暂留的几个判别准则,并在状态常返的情形下进一步研究了状态的正常返与零常返性。通过将环境随机化,利用环境序列的极限理论得到了这类随机环境中的随机游动状态常返、暂留的判别准则及正常返与零常返的判别准则,所得结论是一些文献结果的推广。

关键词: 随机环境, 常返, 暂留, 正常返, 零常返, 随机游动

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

中图分类号: 

  • O211.62
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[1] 任敏1,2,张光辉1. 右半直线上依分布收敛独立随机环境中随机游动的吸收概率[J]. J4, 2013, 48(1): 93-99.
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