LEADER 03903nam 22005893 450 001 9910964413203321 005 20251117113951.0 010 $a9781470472795 010 $a1470472791 035 $a(MiAaPQ)EBC30222572 035 $a(Au-PeEL)EBL30222572 035 $a(CKB)25289765900041 035 $a(OCoLC)1350687926 035 $a(EXLCZ)9925289765900041 100 $a20221110d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (136 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.280 311 08$aPrint version: Chassagneux, Jean-François A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria Providence : American Mathematical Society,c2022 9781470453756 330 $a"We analyze a class of nonlinear partial differential equations (PDEs) defined on Rd P2pRdq, where P2pRdq is the Wasserstein space of probability measures on Rd with a finite second-order moment. We show that such equations admit a classical solutions for sufficiently small time intervals. Under additional constraints, we prove that their solution can be extended to arbitrary large intervals. These nonlinear PDEs arise in the recent developments in the theory of large population stochastic control. More precisely they are the so-called master equations corresponding to asymptotic equilibria for a large population of controlled players with mean-field interaction and subject to minimization constraints. The results in the paper are deduced by exploiting this connection. In particular, we study the differentiability with respect to the initial condition of the flow generated by a forward-backward stochastic system of McKean-Vlasov type. As a byproduct, we prove that the decoupling field generated by the forward-backward system is a classical solution of the corresponding master equation. Finally, we give several applications to meanfield games and to the control of McKean-Vlasov diffusion processes"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aStochastic analysis 606 $aStochastic control theory 606 $aSystems theory; control -- Stochastic systems and control -- Optimal stochastic control$2msc 606 $aProbability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.)$2msc 606 $aProbability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory$2msc 615 0$aStochastic analysis. 615 0$aStochastic control theory. 615 7$aSystems theory; control -- Stochastic systems and control -- Optimal stochastic control. 615 7$aProbability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.). 615 7$aProbability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory. 676 $a519.2/2 676 $a519.22 686 $a93E20$a60H30$a60K35$2msc 700 $aChassagneux$b Jean-Franc?ois$00 701 $aCrisan$b Dan$0524271 701 $aDelarue$b F$g(Franc?ois)$01864712 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910964413203321 996 $aA Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria$94471617 997 $aUNINA