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.
"Asymptotic Analysis and Extinction in a Stochastic Lotka-Volterra Model." Ann. Appl. Probab. 11 (4) 1263 - 1291, November 2001. https://doi.org/10.1214/aoap/1015345403