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 exponent, that is connected to a local property of the probability density function 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) shows the same long-time behavior, each observable follows indeed the same distribution.

中文翻译：

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统计占用时间以及与非均匀随机游走的局部属性的联系。

我们考虑占用时间的统计信息，原始访问次数以及各种随机过程的生存概率，这些随机过程可以归类为更新过程。我们表明，这些可观测变量的分布可以用单个指数来表征，该指数与过程的概率密度函数的局部属性有关，即在时间t占据原点的概率P（t）。我们测试了两个具有空间非均质转移概率的晶格随机游走的不同模型的结果，其中之一具有非马尔可夫性质，并且与理论相符。通过比较两个系统的分布，我们还表明分布仅取决于原点的占用概率：当P（t）显示相同的长期行为时，