scholarly journals A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION

2016 ◽  
Vol 34 (5_6) ◽  
pp. 421-434
Author(s):  
YOUNG-HO KIM ◽  
CHAN-HO PARK ◽  
MUN-JIN BAE
Keyword(s):  
Approximate Solutions ◽  
Delay Equation ◽  
Differential Delay Equation ◽  
Differential Delay ◽  
Stochastic Differential Delay Equation

scholarly journals Carathéodory’s approximate solution to stochastic differential delay equation

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 2019-2028
Author(s):  
Young-Ho Kim
Keyword(s):  
Approximate Solution ◽  
Growth Condition ◽  
Lipschitz Condition ◽  
Linear Growth ◽  
Approximate Solutions ◽  
Delay Equation ◽  
Differential Delay Equation ◽  
Differential Delay ◽  
Stochastic Differential Delay Equation ◽  
Linear Growth Condition

The main aim of this paper is to discuss Carath?odory?s and Euler-Maruyama?s approximate solutions to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and non-linear growth condition.

scholarly journals Euler-Maruyama approximation of backward doubly stochastic differential delay equations

2016 ◽  
Vol 5 (3) ◽  
pp. 146
Author(s):  
Falah Sarhan ◽  
LIU JICHENG
Keyword(s):  
Numerical Solutions ◽  
Delay Equations ◽  
Delay Equation ◽  
Differential Delay Equation ◽  
True Solution ◽  
Differential Delay ◽  
Doubly Stochastic ◽  
Stochastic Differential Delay Equation ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations

In this paper, we attempt to introduce a new numerical approach to solve backward doubly stochastic differential delay equation ( shortly-BDSDDEs ). In the beginning, we present some assumptions to get the numerical scheme for BDSDDEs, from which we prove important theorem. We use the relationship between backward doubly stochastic differential delay equations and stochastic controls by interpreting BDSDDEs as some stochastic optimal control problems, to solve the approximated BDSDDEs and we prove that the numerical solutions of backward doubly stochastic differential delay equation converge to the true solution under the Lipschitz condition.

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