DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

scholarly journals Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Mean Field ◽  
Partial Differential ◽  
Existence And Uniqueness Results ◽  
Doubly Stochastic ◽  
Uniqueness Results

Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.

scholarly journals Optimal control for stochastic partial differential equations and viscosity solutions of Bellman equations

1991 ◽  
Vol 123 ◽  
pp. 13-37 ◽  
Author(s):  
Makiko Nisio
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Viscosity Solutions ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Infinite Dimensions ◽  
Partial Differential ◽  
Bellman Equations

Recently M. G. Crandall and P. L. Lions developed the viscosity theory on nonlinear equations in infinite dimensions and optimal control in Hilbert spaces, in two series of papers, [1], [4].

scholarly journals Foundations of the Theory of Semilinear Stochastic Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-25
Author(s):  
Stefan Tappe
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Uniqueness Result ◽  
Review Article ◽  
Banach Fixed Point Theorem ◽  
Extended Version ◽  
Partial Differential

The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak, and mild solutions, establish their connections, and review a standard existence and uniqueness result. The proof of the existence result is based on a slightly extended version of the Banach fixed point theorem.

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