论文标题
职业时间和与非均匀随机步行本地特性的连接的统计数据
Statistics of occupation time and connection to local properties of non-homogeneous random walks
论文作者
论文摘要
我们考虑职业时间的统计数据，原点的访问次数以及广泛的随机过程的生存概率，可以将其归类为续签过程。我们表明，这些可观察物的分布可以以单个参数为特征，该参数连接到该过程的概率密度函数（PDF）的局部属性，即，在时间$ t $，$ p（t）$上占据原点的概率。我们测试了两个不同模型的晶格随机步行模型，其在空间不均匀的过渡概率上，这是一种非马克维亚性质的一种，并与理论一致。我们还表明，分布仅通过比较两种系统来取决于它们的职业概率：当$ p（t）$显示相同的长期行为时，每个可观察的可观察到确实遵循相同的分布。
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these observables can be characterized by a single parameter, that is connected to a local property of the probability density function (PDF) of the process, viz., the probability of occupying the origin at time $t$, $P(t)$. We test our results for two different models of lattice random walks with spatially inhomogeneous transition probabilities, one of which of non-Markovian nature, and find good agreement with theory. We also show that the distributions depend only on the occupation probability of the origin by comparing them for the two systems: when $P(t)$ show the same long-time behavior, each observable follows indeed the same distribution.
