2001/06/19 by Satya N. Majumdar, Deepak Dhar · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.64.046123
published as Phys. Rev. E 64, 046123 (2001) · 8 pages revtex
arxiv created 2001/06/19 · openalex publication_date 2001/09/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.