State Key Laboratory of High-efficiency Utilization of Coal and Green Chemical Engineering, Ningxia University, Yinchuan, 750021, China.
Xinhua College, Ningxia University, Yinchuan 750021, China.
Math Biosci Eng. 2020 Sep 29;17(6):6702-6719. doi: 10.3934/mbe.2020349.
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.
本文提出了一个在污染环境下具有马尔可夫链和扩散的新型随机种群模型。在扩散系数满足局部 Lipschitz 条件的情况下，证明了模型不变测度的存在唯一性。此外，还讨论了离散时间 Euler-Maruyama 格式下随机种群模型的数值不变测度的存在唯一性，并证明了数值不变测度在 Wasserstein 距离意义下收敛于相应精确解的不变测度。最后，通过数值模拟验证了理论结果的正确性。
