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arXiv · 2608.06814

Stochastic Homogenization of Non-local Hamilton-Jacobi-Bellman equations

Wenjia Jing·Qi Zhang
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Abstract

In this paper we apply the method of Kosygina, Rezakhanlou and Varadhan (CPAM 2006) to establish stochastic homogenization of Hamilton-Jacobi-Bellman (HJB) equation with a vanishing non-local integro-differential operator and a convex super-linearly growing Hamiltonian in stationary ergodic random medium. Their method, first designed for homogenization of HJB equations with vanishing Laplacian operator, relies on stochastic optimal control representation of the solution, a key construction of approximate super-correctors and the technique of linking diffusion process to abstract diffusion in random media. We show how the procedures can be carried out for HJB equations with jump-diffusion. In particular, for the construction of approximate super-correctors, we represent the non-local integro-differential operator as the divergence of a regular integral operator acting on the gradient.

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Wenjia Jing, Qi Zhang. 2026-08-07. Stochastic Homogenization of Non-local Hamilton-Jacobi-Bellman equations. https://arxiv.org/abs/2608.06814

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