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arXiv · 1207.3758

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

N. V. Krylov
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Abstract

We prove that for any constant $K\geq1$, 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.

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N. V. Krylov. 2012-07-16. On regularity properties and approximations of value functions for stochastic differential games in domains. https://doi.org/10.1214/13-aop848

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