“吃你的饼干”环境中一维随机游动的瞬时/递归和速度
Transience/Recurrence and the speed of a one-dimensional random walk in a "have your cookie and eat it" environment
摘要：
考虑整数上的简单随机游动，其转换机制如下。在每个站点$x$处，向右跳转的概率是$ω(x)\in[\frac12,1)$，直到进程第一次从站点$x$向左跳转，从该时刻向前跳转的概率是$\frac12$。我们调查这个过程中的确定性和平稳，遍历环境$\{ω(x)\}_{x\in Z}$的瞬态/递归特性。在确定性环境中，我们还研究了该过程的速度。
英文摘要：
Consider a simple random walk on the integers with the following transition mechanism. At each site $x$, the probability of jumping to the right is $ω(x)\in[\frac12,1)$, until the first time the process jumps to the left from site $x$, from which time onward the probability of jumping to the right is $\frac12$. We investigate the transience/recurrence properties of this process in both deterministic and stationary, ergodic environments $\{ω(x)\}_{x\in Z}$. In deterministic environments, we also study the speed of the process.
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