Compensated projected Euler-Maruyama method for stochastic differential equations with superlinear jumps

In this paper, we present and analyze a compensated projected Euler-Maruyama method for stochastic differential equations with jumps. A mean square convergence result is derived under a coupled condition. This condition and some reasonable assumptions admit that the jump and diffusion coefficients can be superlinear. Moreover, since the Poisson increment has different moment properties from the Brownian increment, some new techniques are developed for convergence analysis. Finally, some numerical experiments are carried out to confirm the theoretical results. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

In this paper, a compensated projected Euler-Maruyama method for stochastic differential equations with jumps is presented and analyzed. The method achieves mean square convergence under a coupled condition and allows for superlinear jump and diffusion coefficients. New techniques are developed for convergence analysis due to the different moment properties of Poisson and Brownian increments. Numerical experiments confirm the theoretical results.