Joint Probability Distributions for a Class of Non-Markovian Processes

Abstract

We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.

13 pages, 1 figure

References in corpus (2)

• Langevin equations for continuous time Lévy flights
• Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

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