scholarly journals On weak solutions of backward stochastic differential equations

2004 ◽  
Vol 49 (1) ◽  
pp. 70-108 ◽  
Author(s):  
Rainer Buckdahn ◽  
Rainer Buckdahn ◽  
Ганс-Юрген Энгельберт ◽  
Hans-Jurgen Engelbert ◽  
Aurel Rascanu ◽  
...  
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Weak Solutions ◽  
Backward Stochastic Differential Equations

scholarly journals On the continuity of weak solutions of backward stochastic differential equations

10.4213/tvp15 ◽  
2007 ◽  
Vol 52 (1) ◽  
pp. 190-199 ◽  
Author(s):  
Rainer Buckdahn ◽  
Rainer Buckdahn ◽  
Ганс-Юрген Энгельберт ◽  
Hans-Jurgen Engelbert
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Weak Solutions ◽  
Backward Stochastic Differential Equations

WEAK SOLUTIONS OF SEMILINEAR PDEs WITH OBSTACLE(S) IN SOBOLEV SPACES AND THEIR PROBABILISTIC INTERPRETATION VIA THE RFBSDEs AND DRFBSDEs

2008 ◽  
Vol 08 (02) ◽  
pp. 247-269 ◽  
Author(s):  
YOUSSEF OUKNINE ◽  
DJIBRIL NDIAYE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Probabilistic Interpretation ◽  
Penalization Method ◽  
Semilinear Pdes ◽  
Uniqueness Of The Solution

We prove the existence and uniqueness of the solution of a semilinear PDEs with obstacle(s) under Lipschitz condition. We give a probabilistic interpretation of the solution in Sobolev spaces using reflected forward–backward stochastic differential equations, doubly reflected forward–backward stochastic differential equations and the penalization method.

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