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Relaxation time of processes driven by multiplicative noise
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We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.
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HERNÁNDEZ MACHADO, Aurora, SAN MIGUEL RUIBAL, Maximino and SANCHO, José M. Relaxation time of processes driven by multiplicative noise. Physical Review A. 1984. Vol. 29, num. 6, pags. 3388-3396. ISSN 1050-2947. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/9344