Stochastic Homogenization for Some Nonlinear Integro-Differential Equations

Details Stochastic Homogenization for Some Nonlinear Integro-Differential Equations Stochastic Homogenization for Some Nonlinear Integro-Differential Equations

2011-01-31

arxiv.org/abs/1101.6052v2

Mathematics

Analysis of PDEs

22 pages; fixed some typos

Scientific paper

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.

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