1.

Record Nr.

UNINA9910964413203321

Autore

Chassagneux Jean-François

Titolo

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

Pubbl/distr/stampa

Providence : , : American Mathematical Society, , 2022

©2022

ISBN

9781470472795

1470472791

Edizione

[1st ed.]

Descrizione fisica

1 online resource (136 pages)

Collana

Memoirs of the American Mathematical Society ; ; v.280

Classificazione

93E2060H3060K35

Altri autori (Persone)

CrisanDan

DelarueF (François)

Disciplina

519.2/2

519.22

Soggetti

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

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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"--