Stochastic Homogenization for Some Nonlinear Integro-Differential Equations
Analysis of PDEs
2012-09-11 v3 Systems and Control
Optimization and Control
Probability
Abstract
In this note we extend to the random, stationary ergodic setting previous results of periodic homogenization for a particular family of nonlinear nonlocal "elliptic" equations with oscillatory coefficients. Such equations include, but are not limited to Bellman equations and the Isaacs equations for the control and differential games of some pure jump processes. The existence of an effective equation and convergence the solutions of the family of the original equations is obtained. Even in the linear case of the equations contained herein the results appear to be new.
Cite
@article{arxiv.1101.6052,
title = {Stochastic Homogenization for Some Nonlinear Integro-Differential Equations},
author = {Russell W. Schwab},
journal= {arXiv preprint arXiv:1101.6052},
year = {2012}
}
Comments
24 pages; fixed some typos; rearranged the presentation in first 2 sections