Asymptotic Analysis and Extinction in a Stochastic Lotka-Volterra Model

Abstract

A stochastic Lotka–Volterra model is formulated by using the semimartingale approach. The large deviation principle is established, and is used to obtain a bound for the asymptotics of the time to extinction of prey population. The bound is given in terms of past-dependent ODE’s closely related to the dynamics of the deterministic Lotka –Volterra model.