Residence Time Distribution for a Class of Gaussian Markov Processes

Abstract

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.

7 pages, RevTex, 1 figure, Journal references added

References in corpus (5)

• Large deviations and nontrivial exponents in coarsening systems
• Persistence with Partial Survival
• Diffusive persistence and the `sign-time' distribution
• Block persistence
• Global Persistence in Directed Percolation

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