title: Persistence of a continuous stochastic process with discrete-time sampling.
abstract: We introduce the concept of "discrete-time persistence," which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T=n Delta T. For a Gaussian Markov process with relaxation rate mu, we show that the persistence (no crossing) probability decays as [rho(a)](n) for large n, where a = exp(-mu Delta T), and we compute rho(a) to high precision. We also define the concept of "alternating persistence," which corresponds to a<0. For a>1, corresponding to motion in an unstable potential (mu<0), there is a nonzero probability of having no zero-crossings in infinite time, and we show how to calculate it.
authors.affiliation: Laboratoire de Physique Quantique, UMR C5626 du CNRS, Université Paul Sabatier, 31062 Toulouse Cedex, France.
authors.forename: S N
authors.initials: SN
authors.lastname: Majumdar
authors.forename: A J
authors.initials: AJ
authors.lastname: Bray
authors.forename: G C
authors.initials: GC
authors.lastname: Ehrhardt