title: Probability density function method for Langevin equations with colored noise.
abstract: Understanding the mesoscopic behavior of dynamical systems described by Langevin equations with colored noise is a fundamental challenge in a variety of fields. We propose a new approach to derive closed-form equations for joint and marginal probability density functions of state variables. This approach is based on a so-called large-eddy-diffusivity closure and can be used to model a wide class of non-Markovian processes described by the noise with an arbitrary correlation function. We demonstrate the accuracy of the proposed probability density function method for several linear and nonlinear Langevin equations.
authors.affiliation: Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
authors.forename: Peng
authors.initials: P
authors.lastname: Wang
authors.affiliation: Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
authors.forename: Alexandre M
authors.initials: AM
authors.lastname: Tartakovsky
authors.affiliation: University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Tartakovsky
mesh_terms: D008390:Markov Chains; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics