scholarly journals On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations

2017 ◽  
Vol 22 (11) ◽  
pp. 1-21
Author(s):  
Tian Zhang ◽  
◽  
Huabin Chen ◽  
Chenggui Yuan ◽  
Tomás Caraballo ◽  
...  
2019 ◽  
Vol 17 (06) ◽  
pp. 1950014 ◽  
Author(s):  
Yuhao Cong ◽  
Weijun Zhan ◽  
Qian Guo

A class of super-linear stochastic delay differential equations (SDDEs) with variable delay and Markovian switching is considered. The main aim of this paper is to investigate the convergence and stability properties of partially truncated Euler–Maruyama (EM) method applied to the SDDEs with variable delay and Markovian switching under the generalized Khasminskii-type condition.


2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chao Yue ◽  
Chengming Huang

This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical solution under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. In particular, these conditions admit that the diffusion coefficient is highly nonlinear. Furthermore, the obtained results are supported by numerical experiments.


2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yanli Zhou ◽  
Yonghong Wu ◽  
Xiangyu Ge ◽  
B. Wiwatanapataphee

Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. Our analysis and numerical examples show that the proposed scheme of high order is effective and efficient for Monte Carlo simulations for jump-diffusion stochastic delay differential equations.


Sign in / Sign up

Export Citation Format

Share Document