Stochastic homogenization of stable-like process with divergence free drift

TL;DR

This paper investigates the homogenization of stable-like processes with divergence-free drift in ergodic environments, extending previous work by removing boundedness constraints on the drift and stream function.

Contribution

It introduces a novel approach to homogenize stable-like processes with unbounded divergence-free drift in ergodic settings.

Findings

Homogenization results established for unbounded divergence-free drift

Extension of existing models to more general ergodic environments

New techniques for handling unbounded coefficients in stochastic processes

Abstract

In this paper we will study homogenization of for stable-like process with divergence-free drift in ergodic environments. In particular, neither the drift nor the stream function are required to be bounded.