Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps

Yongzhen Pei, Hongfu Yang, Qimin Zhang and Fangfang Shen

Applied Mathematics and Computation, 2018, vol. 320, issue C, 524-534

Abstract: This paper focuses on asymptotic mean-square boundedness of several numerical methods applied to a class of stochastic age-dependent population equations with Poisson jumps. The conditions under which the underlying systems are asymptotic mean-square boundedness are considered. It is shown that the asymptotic mean-square boundedness 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 asymptotic mean-square boundedness under a stepsize constraint. The results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of asymptotic mean-square boundedness. Finally, an example is given for illustration.

Keywords: Asymptotic mean-square boundedness; Compensated numerical methods; Non-compensated numerical methods; Stochastic age-dependent population equations; Poisson jumps (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:524-534

DOI: 10.1016/j.amc.2017.10.030

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