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

2012/04/30 by Н. В. Крылов, N. V. Krylov, Krylov, N. V. · 1 citation
Economics, Econometrics and Finance · Mathematics · Social Sciences · #35J60 #49N70 #91A05 #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC #msc:35J60 #msc:49N70 #msc:91A05

paper · pdf · doi:10.48550/arxiv.1205.0048

26 pages. This is the first article in the series of three. Writing the third one required a revision of this article

openalex publication_date 2012/04/30 · arxiv created 2012/07/16 · arxiv updated 2012/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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