A path integral method for coarse-graining noise in stochastic differential equations with multiple time scales

Document Type

Article

Publication Date

1-1-2011

Abstract

We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation describing the system's evolution on slow time scales. For this purpose, we start from the corresponding path integral representation of the stochastic system and apply a multi-scale expansion to the associated path integral kernel of the corresponding Lagrangian. As a concrete example, we apply this expansion to a system that arises in the study of random dispersion fluctuations in dispersion-managed fiber-optic communications. Moreover, we show that, for this particular example, the new path integration method yields the same result at leading order as an asymptotic expansion of the associated FokkerPlanck equation. © 2010 Elsevier B.V. All rights reserved.

Identifier

78649320089 (Scopus)

Publication Title

Physica D Nonlinear Phenomena

External Full Text Location

https://doi.org/10.1016/j.physd.2010.08.010

ISSN

01672789

First Page

89

Last Page

97

Issue

1

Volume

240

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