Exactly solvable nonlinear model with two multiplicative Gaussian colored noises

A. N. Vitrenko

doi:10.1016/j.physa.2005.04.036

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Exactly solvable nonlinear model with two multiplicative Gaussian colored noises

A. N. Vitrenko

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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.

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A. N. Vitrenko. 2006-02-23. Exactly solvable nonlinear model with two multiplicative Gaussian colored noises. https://doi.org/10.1016/j.physa.2005.04.036

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