Asymptotic $C^{1,γ}$-regularity for value functions to uniformly elliptic dynamic programming principles

Abstract

In this paper we prove an asymptotic C 1,γ -estimate for value functions of stochastic processes related to uniformly elliptic dynamic programming principles. As an application, this allows us to pass to the limit with a discrete gradient and then to obtain a C 1,γ -result for the corresponding limit PDE.