On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains
Optimization and Control
2012-07-17 v2
Abstract
We prove the dynamic programming principe 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.
Keywords
Cite
@article{arxiv.1205.0048,
title = {On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains},
author = {N. V. Krylov},
journal= {arXiv preprint arXiv:1205.0048},
year = {2012}
}
Comments
26 pages. This is the first article in the series of three. Writing the third one required a revision of this article