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

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  • Krylov, N.V.

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.

Suggested Citation

  • Krylov, N.V., 2014. "On the independence of the value function for stochastic differential games of the probability space," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4224-4243.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4224-4243
    DOI: 10.1016/j.spa.2014.07.021
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    References listed on IDEAS

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    1. Krylov, N.V., 2013. "On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3273-3298.
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