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Strong convergence of the split-step \(\theta\)-method for stochastic age-dependent capital system with Poisson jumps and fractional Brownian motion. (English) Zbl 1448.65011

Summary: 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 \(\theta\)-method (SS\(\theta\)) 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\(\theta\) method has better accuracy than the Euler method.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65L20 Stability and convergence of numerical methods for ordinary differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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