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On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains

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  • Krylov, N.V.

Abstract

We prove the dynamic programming principle for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order “coefficient” and the “free” term are only assumed to be measurable. In contrast with previous results established for constant stopping times we allow arbitrary stopping times and randomized ones as well. The main assumption, which will be removed in a subsequent article, is that there exists a sufficiently regular solution of the Isaacs equation.

Suggested Citation

  • Krylov, N.V., 2013. "On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3273-3298.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:8:p:3273-3298
    DOI: 10.1016/j.spa.2013.03.004
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    Cited by:

    1. Krylov, N.V., 2014. "On the independence of the value function for stochastic differential games of the probability space," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4224-4243.
    2. Krylov, N.V., 2015. "Approximating the value functions for stochastic differential games with the ones having bounded second derivatives," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 254-271.

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