Stochastic averaging for a completely integrable Hamiltonian system with fractional Brownian motion

Ruifang Wang, Yong Xu, Bin Pei

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper proposes an effective approximation result for the behavior of a small transversal perturbation to a completely integrable stochastic Hamiltonian system on a symplectic manifold. We derive an averaged stochastic differential equations (SDEs) in the action space for the action component of the perturbed system, where the averaged drift coefficient is characterized by the averages of that of the action component with respect to the invariant measure of the unperturbed system on the corresponding invariant manifolds. Then, the averaging principle is shown to be valid such that the action component of the perturbed system converges to the solution of averaged SDEs in the mean square sense.

Original languageEnglish
Article number2350026
JournalStochastics and Dynamics
Volume23
Issue number4
DOIs
StatePublished - 1 Jun 2023

Keywords

  • Averaging principle
  • completely integrable Hamiltonian system
  • fractional Brownian motion
  • generalized Riemann-Stieltjes integral

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