On the independence of the value function for stochastic differential games of the probability space

2014/04/11 by Н. В. Крылов, N. V. Krylov, Krylov, N. V.
Economics, Econometrics and Finance · Engineering · Mathematics · #35D40 #49L25 #49N70 #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.PR #msc:35D40 #msc:49L25 #msc:49N70

paper · pdf · doi:10.48550/arxiv.1404.2972

22 pages. arXiv admin note: text overlap with arXiv:1205.0048

arxiv created 2014/04/11 · openalex publication_date 2014/04/11 · arxiv updated 2014/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the value function in a stochastic differential game does not change if we keep the same space (Ω,F) but introduce probability measures by means of Girsanov's transformation \em depending on the policies of the players. We also show that the value function does not change if we allow the driving Wiener processes to depend on the policies of the players. Finally, we show that the value function does not change if we perform a random time change with the rate depending on the policies of the players.

Citations

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

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