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

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  • Pei, Yongzhen
  • Yang, Hongfu
  • Zhang, Qimin
  • Shen, Fangfang

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.

Suggested Citation

  • Pei, Yongzhen & Yang, Hongfu & Zhang, Qimin & Shen, Fangfang, 2018. "Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 524-534.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:524-534
    DOI: 10.1016/j.amc.2017.10.030
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    References listed on IDEAS

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    1. Tan, Jianguo & Rathinasamy, A. & Pei, Yongzhen, 2015. "Convergence of the split-step θ-method for stochastic age-dependent population equations with Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 305-317.
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    Cited by:

    1. Shi, Chunmei, 2021. "The convergence and stability of full discretization scheme for stochastic age-structured population models," Applied Mathematics and Computation, Elsevier, vol. 396(C).

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    1. Shi, Chunmei, 2021. "The convergence and stability of full discretization scheme for stochastic age-structured population models," Applied Mathematics and Computation, Elsevier, vol. 396(C).

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