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

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)2161-2196
Number of pages36
JournalAnnals of Probability
Volume42
Issue number5
DOIs
StatePublished - Sep 2014

Keywords

  • Isaacs equation
  • Smoothness of value functions
  • Stochastic differential games

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