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portada Distribution Dependent Stochastic Differential Equations
Type
Physical Book
Author
Publisher
Language
English
Pages
350
Format
Hardcover
ISBN13
9789811280146
Categories

Distribution Dependent Stochastic Differential Equations

Feng-Yu Wang (Author) · Panpan Ren (Author) · World Scientific Publishing Company · Hardcover

Distribution Dependent Stochastic Differential Equations - Wang, Feng-Yu ; Ren, Panpan

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Synopsis "Distribution Dependent Stochastic Differential Equations"

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. To restrict a DDSDE in a domain, we consider the reflection boundary by following the line of A V Skorohod (1961).This book provides a self-contained account on singular SDEs and DDSDEs with or without reflection. It covers well-posedness and regularities for singular stochastic differential equations; well-posedness for singular reflected SDEs; well-posedness of singular DDSDEs; Harnack inequalities and derivative formulas for singular DDSDEs; long time behaviors for DDSDEs; DDSDEs with reflecting boundary; and killed DDSDEs.

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