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.
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