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 language | English (US) |
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Pages (from-to) | 2161-2196 |
Number of pages | 36 |
Journal | Annals of Probability |
Volume | 42 |
Issue number | 5 |
DOIs | |
State | Published - Sep 2014 |
Keywords
- Isaacs equation
- Smoothness of value functions
- Stochastic differential games