A pde approach to small stochastic perturbations of Hamiltonian flows

4Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

In this note we present a unified approach, based on pde methods, for the study of averaging principles for (small) stochastic perturbations of Hamiltonian flows in two space dimensions. Such problems were introduced by Freidlin and Wentzell and have been the subject of extensive study in the last few years using probabilistic arguments. When the Hamiltonian flow has critical points, it exhibits complicated behavior near the critical points under a small stochastic perturbation. Asymptotically the slow (averaged) motion takes place on a graph. The issues are to identify both the equations on the sides and the boundary conditions at the vertices of the graph. Our approach is very general and applies also to degenerate anisotropic elliptic operators which could not be considered using the previous methodology. © 2011 Elsevier Inc..

Cite

CITATION STYLE

APA

Ishii, H., & Souganidis, P. E. (2012). A pde approach to small stochastic perturbations of Hamiltonian flows. Journal of Differential Equations, 252(2), 1748–1775. https://doi.org/10.1016/j.jde.2011.08.036

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free