title: Persistence in a stationary time series.
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.
authors.affiliation: Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India.
authors.forename: S N
authors.initials: SN
authors.lastname: Majumdar
authors.forename: D
authors.initials: D
authors.lastname: Dhar