Asymptotic \(C^{1,\gamma}\)-regularity for value functions to uniformly elliptic dynamic programming principles. (English) Zbl 1527.91011
Summary: In this paper we prove an asymptotic \(C^{1,\gamma}\)-estimate for value functions of stochastic processes related to uniformly elliptic dynamic programming principles. As an application, this allows us to pass to the limit with a discrete gradient and then to obtain a \(C^{1,\gamma}\)-result for the corresponding limit PDE.
MSC:
| 91A15 | Stochastic games, stochastic differential games |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 90C39 | Dynamic programming |
References:
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