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Numerical approximation of a stochastic age‐structured population model in a polluted environment with Markovian switching
Author(s) -
Li Wenrui,
Ye Ming,
Zhang Qimin,
Li Yan
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22488
Subject(s) - mathematics , moment (physics) , convergence (economics) , markov process , population model , population , markov chain , rate of convergence , stochastic modelling , mathematical optimization , statistics , computer science , computer network , channel (broadcasting) , physics , demography , classical mechanics , sociology , economics , economic growth
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.