Residence Time Distribution for a Class of Gaussian Markov Processes

Details Residence Time Distribution for a Class of Gaussian Markov Processes Residence Time Distribution for a Class of Gaussian Markov Processes

1999-01-31

arxiv.org/abs/cond-mat/9902004v3

Physics

Condensed Matter

Statistical Mechanics

7 pages, RevTex, 1 figure, Journal references added

Scientific paper

10.1103/PhysRevE.59.6413

We study the distribution of residence time or equivalently that of ``mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter $\alpha$. The persistence exponent for these processes is simply given by $\theta=\alpha$ but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as $\theta$ increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary $\alpha$. For some special values of $\alpha$, we obtain closed form expressions of the distribution function.

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