直线上随机环境中可逗留的随机游动的若干性质

Some Properties of Random Walks with Resting State on the Line in Random Environments

主要研究直线上随机环境中可逗留的随机游动的常返性与极限性质,在独立随机环境下,通过强大数定律给出了常返与暂留的一个充分条件;在一般随机环境下,通过数列的有界性给出了常返与零常返的充分条件并讨论了在独立随机环境下非常返性中的大数定律,从而推广了Solomon的研究框架.

In this paper, we mainly deal with recurrence and limit theorem of random walks with resting state on the line in random environment. In independent random environment, we provide a recurrence-transience sufficient condiction by the strong law of large numbers and study the law of large numbers in the nonrecurrence. In general random environment, we provid some sufficient conditions for recurrence and null recurrence by boundedness of sequence of numbers. So we extend the frame which Solomon has studied.