ON REGULARITY PROPERTIES AND APPROXIMATIONS OF VALUE FUNCTIONS FOR STOCHASTIC DIFFERENTIAL GAMES IN DOMAINS

• 成果类型: Article
• 署名作者: Krylov, N. V.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP848
• 发表日期: 2014
• 页码: 2161-2196
• 关键词: elliptic-equations; EXISTENCE

摘要

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.