Strong convergence of the split-step Emphasis Type="Italic"??/Emphasis-method for stochastic age-dependent capital system with Poisson jumps and fractional Brownian motion

摘要

Most stochastic age-dependent capital systems cannot be solved explicitly, so it is necessary to develop numerical methods and study the properties of numerical solutions. In this paper, we consider a class of stochastic age-dependent capital systems with Poisson jumps and fractional Brownian motion (fBm) and investigate the convergence of the split-step ??-method (SS??) for this system. It is proved that the numerical approximation solutions converge to the analytic solutions for the equations, and the order of approximation is also provided. Finally, a numerical experiment is simulated to illustrate that the SS?? method has better accuracy than the Euler method.