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

Qiang Li, Ting Kang and Qimin Zhang

Applied Mathematics and Computation, 2018, vol. 339, issue C, 81-92

Abstract: 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.

Keywords: Stochastic age-dependent capital system; Mean-square dissipativity; Numerical methods; Fractional Brownian motion; Poisson jumps (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:81-92

DOI: 10.1016/j.amc.2018.07.018

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