Persistence exponent for discrete-time, time-reversible processes

Frank Aurzada; Nadine Guillotin-Plantard

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arXiv · 1502.06799

Persistence exponent for discrete-time, time-reversible processes

Frank Aurzada·Nadine Guillotin-Plantard

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Abstract

We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension with Gaussian scenery. Second, we deal with sums of stationary Gaussian sequences with correlations exhibiting long-range dependence. Apart from the persistence probability we deal with the position of the maximum and the time spent on the positive half-axis by the process.

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Frank Aurzada, Nadine Guillotin-Plantard. 2015-02-24. Persistence exponent for discrete-time, time-reversible processes. https://arxiv.org/abs/1502.06799

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