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

Tobias Schäfer, Richard O. Moore

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)89-97
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume240
Issue number1
DOIs
StatePublished - Jan 1 2011

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • Coarse-graining of noise
  • Fiber optics
  • Multi-scale analysis

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