scholarly journals Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations

Bernoulli ◽  
2006 ◽  
Vol 12 (5) ◽  
pp. 889-916 ◽  
Author(s):  
Jean-Philippe Lemor ◽  
Emmanuel Gobet ◽  
Xavier Warin
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Backward Stochastic Differential Equations ◽  
Regression Method

Optimal Error Estimates for a Fully Discrete Euler Scheme for Decoupled Forward Backward Stochastic Differential Equations

2017 ◽  
Vol 7 (3) ◽  
pp. 548-565
Author(s):  
Bo Gong ◽  
Weidong Zhao
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Error Estimates ◽  
Backward Stochastic Differential Equations ◽  
Optimal Error Estimates ◽  
Euler Scheme ◽  
Optimal Error ◽  
Fully Discrete ◽  
Numerical Approaches

AbstractIn error estimates of various numerical approaches for solving decoupled forward backward stochastic differential equations (FBSDEs), the rate of convergence for one variable is usually less than for the other. Under slightly strengthened smoothness assumptions, we show that the fully discrete Euler scheme admits a first-order rate of convergence for both variables.

scholarly journals High order one-step methods for backward stochastic differential equations via Itô-Taylor expansion

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Quan Zhou ◽  
Yabing Sun
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Taylor Expansion ◽  
Backward Stochastic Differential Equations ◽  
High Order ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
One Step

<p style='text-indent:20px;'>In this work, by combining the Feynman-Kac formula with an Itô-Taylor expansion, we propose a class of high order one-step schemes for backward stochastic differential equations, which can achieve at most six order rate of convergence and only need the terminal conditions on the last one step. Numerical experiments are carried out to show the efficiency and high order accuracy of the proposed schemes.</p>

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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