Klebaner, F.c et R. Liptser,, Asymptotic Analysis and Extinction in a Stochastic Lotka-Volterra Model, Annals of applied probability , 11(4), 2001, pp. 1263-1291
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.