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Residence Time Distribution for a Class of Gaussian Markov Processes

Abhishek Dhar·Satya N. Majumdar
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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 $α$. The persistence exponent for these processes is simply given by $θ=α$ but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as $θ$ 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 $α$. For some special values of $α$, we obtain closed form expressions of the distribution function.

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Abhishek Dhar, Satya N. Majumdar. 1999-02-07. Residence Time Distribution for a Class of Gaussian Markov Processes. https://doi.org/10.1103/physreve.59.6413

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