Mean-square dissipative methods for stochastic age-dependent capital system with fractional Brownian motion and jumps

In this paper, we analyze mean-square dissipativity of numerical methods applied to a class of stochastic age-dependent (vintage) capital system with fractional Brownian motion (fBm) and Poisson jumps. Some sufficient conditions are obtained for ensuring the underlying systems are mean-square dissipative. 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. A numerical example is provided to illustrate the theoretical results.