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

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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.

Original languageEnglish (US)
Pages (from-to)3273-3298
Number of pages26
JournalStochastic Processes and their Applications
Volume123
Issue number8
DOIs
StatePublished - Jan 1 2013

Keywords

  • Dynamic programming principle
  • Isaacs equation
  • Stochastic games

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