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

N. V. Krylov

doi:10.1016/j.spa.2014.07.021

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

N. V. Krylov

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 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.

Original language	English (US)
Pages (from-to)	4224-4243
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	12
DOIs	https://doi.org/10.1016/j.spa.2014.07.021
State	Published - Dec 2014

Bibliographical note

Funding Information:
The author is sincerely grateful to the referee who raised an important question now addressed in the introduction. The author was partially supported by NSF Grant DMS-1160569 .

Keywords

Isaacs equation
Stochastic differential games
Value functions

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AB - 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 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.

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

Abstract

Bibliographical note

Keywords

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