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 = n T. The probability that (n+1) consecutive values of X have the same sign decays as Pn (-θD Tn). We calculate the discrete persistence exponent θD as a series expansion in the correlator C( T) up to 14th order, and extrapolate to T = 0 using constrained Pad\'e approximants to obtain the continuum persistence exponent θ. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.
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