Exactly solvable nonlinear model with two multiplicative Gaussian colored noises

Details Exactly solvable nonlinear model with two multiplicative Gaussian colored noises Exactly solvable nonlinear model with two multiplicative Gaussian colored noises

2006-02-23

arxiv.org/abs/cond-mat/0602535v1

Physica A 359 (2006) 65-74

Physics

Condensed Matter

Statistical Mechanics

15 pages

Scientific paper

10.1016/j.physa.2005.04.036

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 $|x|^{\alpha}$. 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.

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