On regularity properties and approximations of value functions for stochastic differential games in domains

Abstract

We prove that for any constant $K\ge 1$, the value functions for time homogeneous stochastic differential games in the whole space can be approximated up to a constant over $K$ by value functions whose second-order derivatives are bounded by a constant times $K$. On the way of proving this result we prove that the value functions for stochastic differential games in domains and in the whole space admit estimates of their Lipschitz constants in a variety of settings.

Published in at http://dx.doi.org/10.1214/13-AOP848 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• A probabilistic approach to interior regularity of fully nonlinear degenerate elliptic equations in smooth domains
• On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions

Cited by in corpus (2)

• On representation and regularity of viscosity solutions to degenerate Isaacs equations and certain nonconvex Hessian equations
• Boundary regularity for viscosity solutions of fully nonlinear elliptic equations