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随机环境中可逗留随机游动的强极限边界
  • 期刊名称：应用数学 2006,19(2):270-274.
  • 时间：0
  • 分类：O211.9[理学—概率论与数理统计;理学—数学]
  • 作者机构：[1]暨南大学统计学系,广东广州510632, [2]暨南大学数学系,广东广州510632
  • 相关基金：国家自然科学基金（10271120）资助项目;暨南大学校内基金资助项目（600223）
  • 相关项目：排队系统的最优控制及其应用的研究
关键词： 随机环境, 随机游动, 重对数律, 强极限边界, Random environment ； Random walk ； The law of the iterated logrithm , Strong limiting bounds
中文摘要：

假定{（αi，βi），αi，βi∈（0，1），i∈Z）是一列i．i．d．的随机变量，γi=1-αi-βi，称{（αi，γi，βi），i∈Z}为随机环境．在这个环境上定义一个随机游动{Xk}（称为随机环境中可逗留随机游动）：当在x状态时，它以概率αx向右游走一步，以概率βx向左游走一步，或者以概率γx逗留．本文获得了该过程能够游走的最大值的强极限边界．

英文摘要：

Suppose that {（αi,βi）,αi,βi∈（0,1）,i∈Z） are i. i. d. random variables, γi=1-αi-βi·{（αi,γi,βi）,i∈Z} serve as an environment. This environment defines a random walk {Xk} （Called random walk with resting state on the line in a random environment） which,when at x, moves one step to the right with probability αx, and one step to the left with probability βx, or rests with probability γx· strong limiting bounds for maximal excursion and for maximum reached by this processes are obtained.

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