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Persistence in a Stationary Time-series

Satya N. Majumdar·Deepak Dhar
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Abstract

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times. We then construct a specific sequence for which the persistence can be computed even though the sequence is non-Markovian. We show that this may be considered as a limiting case of persistence in the diffusion process on a hierarchical lattice.

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Satya N. Majumdar, Deepak Dhar. 2001-06-19. Persistence in a Stationary Time-series. https://doi.org/10.1103/physreve.64.046123

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