scholarly journals A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients

2004 ◽  
Vol 2004 (6) ◽  
pp. 461-477
Author(s):  
Omid. S. Fard ◽  
Ali V. Kamyad
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Nonlinear Term ◽  
Piecewise Linear ◽  
Backward Stochastic Differential Equation ◽  
Numerical Approach ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Controls ◽  
The Relationship ◽  
Uniformly Continuous

We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE corresponding to the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original nonlinear BSDE.

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.

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