Z上随机环境中确定性驱动的随机游动
Deterministically driven random walks in a random environment on Z
摘要：
我们引入了可数状态空间（DWDE）上确定性环境中确定性游动的概念。对于确定性行走在一个固定的环境中，我们建立的性质类似于那些发现在马尔可夫链理论，但系统一般不具有马尔可夫性。特别是，我们建立的假设，确保$\Z$上的DWDE是复发性的或短暂的。该结果的直接结果是$\Z$上的对称DWDE是循环的。此外，在瞬态的情况下，我们表明，DWDE发散到$+ \infty$的概率是0或1。在某些情况下，我们计算在瞬态情况下的发散方向。
英文摘要：
We introduce the concept of a deterministic walk in a deterministic environment on a countable state space (DWDE). For the deterministic walk in a fixed environment we establish properties analogous to those found in Markov chain theory, but for systems that do not in general have the Markov property. In particular, we establish hypotheses ensuring that a DWDE on $\Z$ is either recurrent or transient. An immediate consequence of this result is that a symmetric DWDE on $\Z$ is recurrent. Moreover, in the transient case, we show that the probability that the DWDE diverges to $+ \infty$ is either 0 or 1. In certain cases we compute the direction of divergence in the transient case.
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