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.
Bibliographical noteFunding Information:
The author was partially supported by the NSF Grant DNS-1160569 . The author is sincerely grateful to the referee for pointing out a few misprints.
- Dynamic programming principle
- Isaacs equation
- Stochastic games