Local regularity estimates for general discrete dynamic programming equations

TL;DR

This paper provides an analytic proof of regularity estimates, including H"older continuity and Harnack's inequality, for solutions to a broad class of discrete dynamic programming equations, extending to Pucci-type inequalities.

Contribution

It introduces a novel analytic approach to establish regularity estimates for general discrete dynamic programming equations, including extremal operators.

Findings

Proves asymptotic H"older estimate for solutions.

Establishes Harnack's inequality in the discrete setting.

Generalizes results to Pucci-type inequalities.

Abstract

We obtain an analytic proof for asymptotic H\"older estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete extremal operators. Thus the results cover a quite general class of equations.