scholarly journals The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations

2015 ◽  
Vol 4 (3) ◽  
pp. 120
Author(s):  
Jie Zhu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Mean Field ◽  
Backward Stochastic Differential Equations ◽  
Partial Differential ◽  
The Mean

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.

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