Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order

1998 ◽  
pp. 79-127 ◽  
Author(s):  
Étienne Pardoux
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Viscosity Solutions ◽  
Backward Stochastic Differential Equations ◽  
Second Order ◽  
Elliptic Pdes ◽  
Semilinear Parabolic

scholarly journals Double-barriers-reflected BSDEs with jumps and viscosity solutions of parabolic integrodifferential PDEs

2005 ◽  
Vol 2005 (1) ◽  
pp. 37-53 ◽  
Author(s):  
N. Harraj ◽  
Y. Ouknine ◽  
I. Turpin
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Viscosity Solutions ◽  
Backward Stochastic Differential Equations ◽  
Probabilistic Interpretation ◽  
Reflected Bsdes

We give a probabilistic interpretation of the viscosity solutions of parabolic integrodifferential partial equations with two obstacles via the solutions of forward-backward stochastic differential equations with jumps.

A Numerical Method and its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations

2014 ◽  
Vol 15 (3) ◽  
pp. 618-646 ◽  
Author(s):  
Weidong Zhao ◽  
Wei Zhang ◽  
Lili Ju
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Error Estimates ◽  
Backward Stochastic Differential Equations ◽  
Second Order ◽  
Numerical Schemes ◽  
Reference Equations ◽  
Taylor Scheme ◽  
Theoretical Results

AbstractIn this paper, a new numerical method for solving the decoupled forward-backward stochastic differential equations (FBSDEs) is proposed based on some specially derived reference equations. We rigorously analyze errors of the proposed method under general situations. Then we present error estimates for each of the specific cases when some classical numerical schemes for solving the forward SDE are taken in the method; in particular, we prove that the proposed method is second-order accurate if used together with the order-2.0 weak Taylor scheme for the SDE. Some examples are also given to numerically demonstrate the accuracy of the proposed method and verify the theoretical results.

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