Abstract
We introduce a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the Mc-Kean-Vlasov-type equations describing nonlinear Markov processes and the Hamilton-Jacobi-Bellman(HJB)-Isaacs equation of stochastic control and games thus allowing for a unified analysis of these equations. This leads to an effective theory of coupled forward-backward systems (forward McKean-Vlasov evolution and backward HJB-Isaacs evolution) that are central to the modern theory of mean-field games.
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