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

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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 languageEnglish (US)
Pages (from-to)4224-4243
Number of pages20
JournalStochastic Processes and their Applications
Volume124
Issue number12
DOIs
StatePublished - 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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