Book
Distribution Dependent Stochastic Differential Equations
ISBN : 9789811280146
Author : Feng-yu Wang
Publisher : World Scientific
Year : 2025
Language : English
Type : Book
Description : Corresponding to the link of Itô's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker–Planck equations. This type of SDEs is named after McKean–Vlasov due to the pioneering work of H P McKean (1966), where an expectation dependent SDE is proposed to characterize nonlinear PDEs for Maxwellian gas. Moreover, by using the propagation of chaos for Kac particle systems, weak solutions of DDSDEs are constructed as weak limits of mean field particle systems when the number of particles goes to infinity, so that DDSDEs are also called mean-field SDEs.
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