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.

No abstract

No abstract

<p style='text-indent:20px;'>In this paper, to approximate the super-linear stochastic differential equations modulated by a Markov chain, we investigate a truncated Milstein method with convergence order 1 in the mean-square sense. Under Khasminskii-type conditions, we establish the convergence result by employing a relationship between local and global errors. Finally, we confirm the convergence rate by a numerical example.</p>

The truncated Euler-Maruyama method is employed together with the Multi-level Monte Carlo method to approximate expectations of some functions of solutions to stochastic differential equations (SDEs). The convergence rate and the computational cost of the approximations are proved, when the coefficients of SDEs satisfy the local Lipschitz and Khasminskiitype conditions. Numerical examples are provided to demonstrate the theoretical results.ARTICLE HISTORY