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On mean field games with common noise and McKean-Vlasov SPDEs
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Kolokoltsov, Vassili N. and Troeva, Marianna (2019) On mean field games with common noise and McKean-Vlasov SPDEs. Stochastic Analysis and Applications, 37 (4). pp. 522-549. doi:10.1080/07362994.2019.1592690 ISSN 0736-2994.
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Official URL: https://doi.org/10.1080/07362994.2019.1592690
Abstract
We formulate the MFG limit for N interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any (regular enough) solution provides an 1/N-Nash-equilibrium profile for the initial N-player game. We use the method of stochastic characteristics to provide the link with the basic models of MFG with a major player. We develop two auxiliary theories of independent interest: sensitivity and regularity analysis for McKean-Vlasov SPDEs and the 1/N-convergence rate for the propagation of chaos property of interacting diffusions.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Stochastic Analysis and Applications | ||||||
Publisher: | Taylor & Francis (Routledge) | ||||||
ISSN: | 0736-2994 | ||||||
Official Date: | 16 April 2019 | ||||||
Dates: |
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Volume: | 37 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 522-549 | ||||||
DOI: | 10.1080/07362994.2019.1592690 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | โThis is an Accepted Manuscript of an article published by Taylor & Francis in Stochastic Analysis and Applications on 16/04/2019, available online: http://www.tandfonline.com/10.1080/07362994.2019.1592690 | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 12 March 2019 | ||||||
Date of first compliant Open Access: | 16 April 2020 | ||||||
Related URLs: | |||||||
Open Access Version: |
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