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Teoriya Veroyatnostei i ee Primeneniya, 2021, Volume 66, Issue 4, Pages 774–805
DOI: https://doi.org/10.4213/tvp5519 (Mi tvp5519) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Controlled diffusion mean field games with common noise and McKean–Vlasov second order backward SDE

A. Barrassoa, N. Touzib

a Université d'Évry Val d'Éssonne, Évry, France
b Ecole Polytechnique, France
Full-text PDF (578 kB) Citations (6)
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DOI: https://doi.org/10.4213/tvp5519
Abstract: We consider a mean field game with common noise in which the diffusion coefficients may be controlled. We prove existence of a weak relaxed solution under some continuity conditions on the coefficients. We then show that, when there is no common noise, the solution of this mean field game is characterized by a McKean–Vlasov type second order backward SDE.
Keywords: stochastic control, Nash equilibrium, mean field game, exterior noise.
Funding agency Grant number
Agence Nationale de la Recherche PACMAN
This work was supported by ANR project PACMAN, the joint lab FiME, the Chaires FiME-FDD, and Financial Risks of the Louis Bachelier Institute.
Received: 30.06.2021
Accepted: 30.06.2021
English version:
Theory of Probability and its Applications, 2022, Volume 66, Issue 4, Pages 613–639
DOI: https://doi.org/10.1137/S0040585X97T990654
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Barrasso, N. Touzi, “Controlled diffusion mean field games with common noise and McKean–Vlasov second order backward SDE”, Teor. Veroyatnost. i Primenen., 66:4 (2021), 774–805; Theory Probab. Appl., 66:4 (2022), 613–639
Citation in format AMSBIB
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\by A.~Barrasso, N.~Touzi
\paper Controlled diffusion mean field games with common noise and McKean--Vlasov second order backward SDE
\jour Teor. Veroyatnost. i Primenen.
\yr 2021
\vol 66
\issue 4
\pages 774--805
\mathnet{http://mi.mathnet.ru/tvp5519}
\crossref{https://doi.org/10.4213/tvp5519}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4331220}
\zmath{https://zbmath.org/?q=an:1483.91029}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 66
\issue 4
\pages 613--639
\crossref{https://doi.org/10.1137/S0040585X97T990654}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129598717}
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  • https://doi.org/10.4213/tvp5519
  • https://www.mathnet.ru/eng/tvp/v66/i4/p774
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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