黎曼流形上的抽象McKean-Vlasov和HJB方程及其分数阶形式和相关的正倒向方程组
Abstract McKean-Vlasov and HJB equations, their fractional versions and related forward-backward systems on Riemannian manifolds
摘要：
本文在巴拿赫空间中引入了一类抽象的非线性分数阶伪微分方程，它既包括描述非线性Markov过程的Mc-Kean-Vlasov型方程，又包括随机控制和对策的Hamilton-Jacobi-Bellman（HJB）-Isaacs方程，从而使这些方程得到统一的分析.这导致了一个有效的耦合前向-后向系统理论（前向McKean-Vlasov演化和后向HJB-Isaacs演化），这是现代平均场博弈理论的核心。
英文摘要：
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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