In this paper, a stochastic age‐structured population model with Markovian switching is investigated in a polluted environment. Both the stochastic disturbance of environment and the Markovian switching are incorporated into the model. By Itô formula and several assumptions, the boundedness in the qth moment of exact solutions of model are proved. Furthermore, making use of truncated Euler–Maruyama (EM) method, the strong convergence criterion of numerical approximation in the qth moment is established, and the rate of convergence is estimated. Numerical simulations are carried out to illustrate the theoretical results. Our results indicate that the truncated EM method can be used for stochastic age‐structured population system in a polluted environment.

中文翻译：

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马尔可夫切换的污染环境下年龄结构随机种群模型的数值逼近

本文研究了在污染环境下具有马尔可夫切换的随机年龄结构人口模型。环境的随机干扰和马尔可夫切换都被纳入模型。通过Itô公式和几个假设，证明了模型精确解在第q时刻的有界性。此外，利用截短的Euler–Maruyama（EM）方法，建立了q时刻数值逼近的强收敛准则，并估计了收敛速度。进行了数值模拟以说明理论结果。我们的结果表明，在受污染的环境中，截断的EM方法可用于年龄结构随机的人口系统。