title: Series expansion calculation of persistence exponents.
abstract: We consider an arbitrary Gaussian stationary process X(T) with known correlator C(T), sampled at discrete times Tn = nDeltaT. The probability that (n+1) consecutive values of X have the same sign decays as Pn approximately exp(-theta(D)Tn). We calculate the discrete persistence exponent theta(D) as a series expansion in the correlator C(DeltaT) up to fourteenth order, and extrapolate to DeltaT = 0 using constrained Padé approximants to obtain the continuum persistence exponent thetas. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.
authors.affiliation: Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: George C M A
authors.initials: GC
authors.lastname: Ehrhardt
authors.forename: Alan J
authors.initials: AJ
authors.lastname: Bray