Distribution Dependent Stochastic Differential Equations (World Scientific Series on Probability Theory and Its Applications)

Wang, Feng-yu; Ren, Panpan

ISBN 10: 9811280142 / ISBN 13: 9789811280146

Published by WSPC, 2024

About this Item

Seller Inventory # I-9789811280146

Bibliographic Details

• Title: Distribution Dependent Stochastic Differential Equations (World Scientific Series on Probability Theory and Its Applications)
• Publisher: WSPC
• Publication Date: 2024
• Language: English
• ISBN 10: 9811280142
• ISBN 13: 9789811280146
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.