Approximation of invariant measure for a stochastic population model with Markov chain and diffusion in a polluted environment

In the paper, we propose a novel stochastic population model with Markov chain and diffusion in a polluted environment. Under the condition that the diffusion coefficient satisfies the local Lipschitz condition, we prove the existence and uniqueness of invariant measure for the model. Moreover, we also discuss the existence and uniqueness of numerical invariance measure for stochastic population model under the discrete-time Euler-Maruyama scheme, and prove that numerical invariance measure converges to the invariance measure of the corresponding exact solution in the Wasserstein distance sense. Finally, we give the numerical simulation to show the correctness of the theoretical results.