Convergence and stability of implicit compensated Euler method for stochastic differential equations with Poisson random measure

摘要

In this paper, an implicit compensated Euler method is introduced for stochastic differential equations with Poisson random measure. A convergence theorem is proved to show that the method obtains a strong order 0.5. After exploiting the conditions of exponential mean-square stability of such equations, the implicit compensated Euler method is proved to share the same stability for any step size. Numerical examples indicate the performance of the convergence and stability.