Convergence of numerical solutions to stochastic delay differential equations with jumps

This paper studies a class of stochastic delay differential equations with jumps (SDDEJs). Explicit solutions can hardly be obtained for the SDDEJs. Appropriate numerical approximation schemes such as the Euler scheme are needed to apply SDDEJs in practice or to study their properties. In this paper, it is proved that the Euler approximation solutions converge to the analytic solution for SDDEJs under weaker conditions than the linear growth condition and global Lipschitz condition. An example is given for illustration.