A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria

• Autore: Chassagneux Jean-François
• Pubblicazione: Providence : , : American Mathematical Society, , 2022; ©2022
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (136 pages)
• Disciplina: 519.2/2; 519.22
• Soggetto topico: Stochastic analysis; Stochastic control theory; Systems theory; control -- Stochastic systems and control -- Optimal stochastic control; Probability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.); Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory
• Classificazione: 93E2060H3060K35
• Altri autori: CrisanDan DelarueF (François)
• Sommario/riassunto: "We analyze a class of nonlinear partial differential equations (PDEs) defined on Rd P2pRdq, where P2pRdq is the Wasserstein space of probability measures on Rd with a finite second-order moment. We show that such equations admit a classical solutions for sufficiently small time intervals. Under additional constraints, we prove that their solution can be extended to arbitrary large intervals. These nonlinear PDEs arise in the recent developments in the theory of large population stochastic control. More precisely they are the so-called master equations corresponding to asymptotic equilibria for a large population of controlled players with mean-field interaction and subject to minimization constraints. The results in the paper are deduced by exploiting this connection. In particular, we study the differentiability with respect to the initial condition of the flow generated by a forward-backward stochastic system of McKean-Vlasov type. As a byproduct, we prove that the decoupling field generated by the forward-backward system is a classical solution of the corresponding master equation. Finally, we give several applications to meanfield games and to the control of McKean-Vlasov diffusion processes"--
• Titolo autorizzato: A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria
• ISBN: 9781470472795; 1470472791
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910964413203321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society