eng
Science and Education Publishing
Journal of Mathematical Sciences and Applications
2333-8792
2016-04-13
4
1
20
28
10.12691/jmsa-4-1-4
JMSA2016414
article
Numerical Solution of Nonlinear Stochastic Differential Delay Equation with Markovian Switching
Chaozhu Hu
huchaozhu@126.cn
1
Shaobo Zhou
2
School of Science, Hubei University of Technology, Wuhan 430068, Hubei, China
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China
This paper is concerned with the Euler-Maruyama approximate solution of nonlinear stochastic delay differential equations with Markovian switching (SDDEwMSs). We establish the existence and uniqueness results for the global solution of SDDEwMSs under the polynomial growth and the local Lipschitz condition. we then introduce Euler-Maruyama approximate solution of this equation, and establish the convergence in probability of the numerical solution to the exact solution of the problem without the linear growth condition. As an application, we also give one example to demonstrate our results.
http://pubs.sciepub.com/jmsa/4/1/4/jmsa-4-1-4.pdf
stochastic differential delay equation
Euler-Maruyama
convergence in probability
markovian switching