Mean-square dissipativity of several numerical methods for stochastic differential equations with jumps

This paper focuses on mean-square dissipativity of several numerical methods applied to a class of stochastic differential equations with jumps. The conditions under which the underlying systems are mean-square dissipative are given. It is shown that the mean-square dissipativity is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce mean-square dissipativity under a stepsize constraint. Those results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of mean-square dissipativity.