Abstract McKean-Vlasov and HJB equations, their fractional versions and related forward-backward systems on Riemannian manifolds

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.

Submitted for publication to MIAN Proceedings, v. 315

References in corpus (4)

• On the mean field games with common noise and the McKean-Vlasov SPDEs
• On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations
• Strong Short Time Asymptotics and Convolution Approximation of the Heat Kernel
• Regularity and Sensitivity for McKean-Vlasov SPDEs