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SUMMARY:Fractional forward-backward systems of Banach-space valued HJB and
  McKean-Vlasov equations arising in fractional mean-field games - Vassili 
 Kolokoltsov (University of Warwick)
DTSTART:20220421T123000Z
DTEND:20220421T133000Z
UID:TALK171398@talks.cam.ac.uk
DESCRIPTION:We introduce a class of abstract nonlinear fractional pseudo-d
 ifferential equations in Banach spaces that includes both the Mc-Kean-Vlas
 ov-type equations describing nonlinear Markov processes and the Hamilton-J
 acobi-Bellman(HJB)-Isaacs equation of stochastic control and games thus al
 lowing for a unified analysis of these equations. This leads to an effecti
 ve theory of coupled forward-backward systems (forward McKean-Vlasov evolu
 tion and backward HJB-Isaacs evolution) that are central to the modern the
 ory of mean-field games. Related questions concern the study of Hilbert-sp
 ace valued Mc-Kean-Vlasov diffusion. The estimates of growth are shown to 
 be expressed (even for non-fractional diffusions) in terms of the Mittag-L
 effler and Le Roy functions.\n(Based on the joint work with M.S. Troeva).
LOCATION:Seminar Room 1\, Newton Institute
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