Stationary distribution of stochastic population dynamics in state-dependent random environments

摘要

This work studies the stationary distribution of stochastic Lotka-Volterra population dynamics in state-dependent random environments. We first use the stochastic comparison approach to handle the difficulty caused by the state-dependent regime-switching. Then the ergodic property and positive recurrence are investigated by the theory of M-matrix under small perturbation. The mean of the stationary distribution is also estimated. At last, the main results are illustrated by a numerical example. (C) 2020 Elsevier B.V. All rights reserved.