Abstract

We study a class of Lotka–Volterra stochastic differential equations with continuous and pure-jump noise components, and derive conditions that guarantee the strong stochastic persistence (SSP) of the populations engaged in the ecological dynamics. More specifically, we prove that, under certain technical assumptions on the jumpsizes and rates, there is convergence of the laws of the stochastic process to a uniquestationary distribution supported far away from extinction. We show how the tech-niques and conditions used in proving SSP for general Kolmogorov systems driven solely by Brownian motion must be adapted and tailored in order to account for the jumps of the driving noise. We provide examples of applications to the case where the underlying food-web is: (a) a 1-predator, 2-prey food-web, and (b) a multi-layer food-chain.