On the adjoint Markov policies in stochastic differential games

N. V. Krylov

Research output: Contribution to journalArticlepeer-review


We consider time-homogeneous uniformly non degenerate stochastic differential games in domains and propose constructing ε-optimal strategies and policies by using adjoint Markov strategies and adjoint Markov policies which are actually time-homogeneous Markov, however, relative not to the original process but to a couple of processes governed by a system consisting of the main original equation and of an adjoint stochastic equations of the same type as the main one. We show how to find ε-optimal strategies and policies in these classes by using the solvability in Sobolev spaces of not the original Isaacs equation but of its appropriate modification. We also give an example of a uniformly nondegenerate game where our assumptions are not satisfied and where we conjecture that there are no not only optimal Markov but even ε-optimal adjoint (time-homogeneous) Markov strategies for one of the players.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalCommunications on Stochastic Analysis
Issue number1
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© Serials Publications Pvt. Ltd.


  • Isaacs equation
  • Stochastic differential games
  • Value functions


Dive into the research topics of 'On the adjoint Markov policies in stochastic differential games'. Together they form a unique fingerprint.

Cite this