Ornstein–Uhlenbeck process with fluctuating damping
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This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the dichotomous noise and fractional Gaussian noise are considered. Their solutions are obtained explicitly, with the expressions of the mean and covariance determined explicitly. Properties of the mean and covariance of the Ornstein-Uhlenbeck process with random damping, in particular the asymptotic behavior, are studied. The effect of the multiplicative noise on the stability property of the resulting processes is investigated.
22 pages, 5 figures, accepted to be published in Physica A
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multiplicative noise, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Mathematical Physics (math-ph), QA273-280 Probabilities. Mathematical statistics, Langevin equation, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, fractional Gaussian noise, Ornstein-Uhlenbeck process, Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.), Condensed Matter - Statistical Mechanics, Mathematical Physics, dichotomous noise
multiplicative noise, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Mathematical Physics (math-ph), QA273-280 Probabilities. Mathematical statistics, Langevin equation, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, fractional Gaussian noise, Ornstein-Uhlenbeck process, Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.), Condensed Matter - Statistical Mechanics, Mathematical Physics, dichotomous noise
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