Persistence in a Stationary Time-series

Details Persistence in a Stationary Time-series Persistence in a Stationary Time-series

2001-06-19

arxiv.org/abs/cond-mat/0106365v1

Phys. Rev. E 64, 046123 (2001)

Physics

Condensed Matter

Statistical Mechanics

8 pages revtex

Scientific paper

10.1103/PhysRevE.64.046123

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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