scholarly journals Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Minghui Song ◽  
Hui Yu
Keyword(s):  
Numerical Solutions ◽  
Random Measure ◽  
Global Solutions ◽  
Euler Method ◽  
Delay Equations ◽  
Poisson Random Measure ◽  
Differential Delay ◽  
Numerical Example ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations

The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. Numerical example is given to indicate our results.

scholarly journals Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hua Yang ◽  
Feng Jiang
Keyword(s):  
Diffusion Coefficients ◽  
Numerical Solutions ◽  
Delay Equations ◽  
Markovian Switching ◽  
Analytic Approximation ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Poisson Jump ◽  
And Diffusion

We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs). Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJMSs when the drift and diffusion coefficients are Taylor approximations.

scholarly journals Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuaibin Gao ◽  
Junhao Hu
Keyword(s):  
Numerical Solutions ◽  
Delay Equations ◽  
Markovian Switching ◽  
Type Condition ◽  
Differential Delay ◽  
Almost Sure Exponential Stability ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Highly Nonlinear ◽  
Strong Convergence Rate

AbstractIn this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type 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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