Stochastic equation for a jumping process with long-time correlations

Details Stochastic equation for a jumping process with long-time correlations Stochastic equation for a jumping process with long-time correlations

2004-05-12

arxiv.org/abs/cond-mat/0405249v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 5 Postscript figures

Scientific paper

10.1103/PhysRevE.70.051102

A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is characterized by the power-law autocorrelation function. Therefore, it can serve as a model of the 1/f noise as well as a model of the stochastic force in the generalized Langevin equation. This equation is solved for the noise correlations 1/t; the resulting velocity distribution has sharply falling tails. The system preserves the memory about the initial condition for a very long time.

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