Exactly solvable nonlinear model with two multiplicative Gaussian colored noises

A.N. Vitrenko

Physica A: Statistical Mechanics and its Applications, 2006, vol. 359, issue C, 65-74

Abstract: An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state x as x and |x|α. An exactly soluble model of a system is constructed due to consideration of a specific relation between noises. Exact expressions for the time-dependent univariate probability distribution function and the fractional moments are derived. Their long-time asymptotic behavior is investigated analytically. It is shown that anomalous diffusion and stochastic localization of particles, not subjected to a restoring force, can occur.

Keywords: Colored noises; Gaussian processes; Statistical properties; Anomalous diffusion (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:359:y:2006:i:c:p:65-74

DOI: 10.1016/j.physa.2005.04.036

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