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Stationary Distribution of Stochastic Age-Dependent Population–Toxicant Model with Markov Switching

Author

Listed:
  • Yanyan Du

    (School of Science, Qingdao University of Technology, Qingdao 266520, China)

  • Zong Wang

    (School of Science, Qingdao University of Technology, Qingdao 266520, China)

Abstract

This work focuses on the convergence of the numerical invariant measure for a stochastic age-dependent population–toxicant model with Markov switching. Considering that Euler–Maruyama (EM) has the advantage of fast computation and low cost, explicit EM was used to discretize the time variable. With the help of the p -th moment boundedness of the analytical and numerical solutions of the model, the existence and uniqueness of the corresponding invariant measures were obtained. Under suitable assumptions, the conclusion that the numerical invariant measure converges to the invariant measure of the analytic solution was proven by defining the Wasserstein distance. A numerical simulation was performed to illustrate the theoretical results.

Suggested Citation

  • Yanyan Du & Zong Wang, 2024. "Stationary Distribution of Stochastic Age-Dependent Population–Toxicant Model with Markov Switching," Mathematics, MDPI, vol. 12(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1212-:d:1377732
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    References listed on IDEAS

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    1. Zhao, Yu & Yuan, Sanling & Zhang, Qimin, 2015. "Numerical solution of a fuzzy stochastic single-species age-structure model in a polluted environment," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 385-396.
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