Stationary distribution of stochastic population dynamics in state-dependent random environments
This study focuses on the Lotka-Volterra stochastic population systems in random state-dependent environments that are characterized by a stochastic differential equation (SDE). The authors emphasize the ergodicity and positive recurrence of SDEs with regime-switching, from which the existence and uniqueness of a stationary distribution follows. A stochastic comparison approach is presented for controlling state-dependent regime-switching processes with a finite state space. To ensure sufficient conditions for ergodicity and positive repeatability, the M-matrix theory is used and the average value of the stationary distribution of the population system is investigated. At the end of the article, a numerical example is presented to illustrate the results obtained.
scientific article; zbMATH DE number 7290541