Exactly solvable nonlinear model with two multiplicative Gaussian colored noises
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Date
2006
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Elsevier
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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.
Keywords
кольорові шуми, цветные шумы, colored noises, гаусівські процеси, гауссовские процессы, gaussian processes, статистичні властивості, статистические свойства, statistical properties, аномальна дифузія, аномальная диффузия, anomalous diffusion
Citation
Exactly solvable nonlinear model with two multiplicative Gaussian colored noises [Text] / A.N. Vitrenko // Physica A: Statistical Mechanics and its Applications. – 2006. – Vol. 359. – P. 65-74.