Numerical approximation of a stochastic age‐structured population model in a polluted environment with Markovian switching
Wenrui Li, Ming Ye, Qimin Zhang, Yan Li
Abstract
Abstract 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 q th 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 q th 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.