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

2022/06/17 by Blanc, Pablo, Parviainen, Mikko, Rossi, Julio D.
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2206.09001

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.

Related

• Hölder regularity for stochastic processes with bounded and measurable increments
• Asymptotic Hölder Regularity for the Ellipsoid Process
• Discrete stochastic maximal regularity
• Regularity for nonlinear stochastic games
• Local regularity estimates for general discrete dynamic programming equations