V. Krylov, N., On regularity properties and approximations of value functions for stochastic differential games in domains, Annals of probability , 42(5), 2014, pp. 2161-2196
We prove that for any constant K.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.