Distribution Dependent Stochastic Differential Equations
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A01=Feng-yu Wang
A01=Panpan Ren
Age Group_Uncategorized
Age Group_Uncategorized
Author_Feng-yu Wang
Author_Panpan Ren
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Bismut Type Derivative Formulas
Category1=Non-Fiction
Category=PBKJ
Category=PBWL
COP=Singapore
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Distribution Dependent SDEs
eq_isMigrated=0
eq_isMigrated=2
eq_nobargain
Ergodicity
Harnack Inequalities
Killed Distribution Dependent SDEs
Language_English
Large Deviations
PA=Available
Price_€100 and above
PS=Forthcoming
Reflected Stochastic Systems
Singular Stochastic Systems
softlaunch
Product details
- ISBN 9789811280146
- Publication Date: 01 Nov 2024
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
- Language: English
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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.
