Numerical Solution of Stochastic Differential Equations by use of Path Integration: A study of a stochastic Lotka-Volterra model

Abstract

Some theory of real and stochastic analysis in order to introduce the Path Integration method in terms of stochastic operators. A theorem presenting sufficient conditions for convergence of the Path Integration method is then presented. The solution of a stochastic Lotka-Volterra model of a prey-predator relationship is then discussed, with and without the predator being harvested. And finally, an adaptive algorithm designed to solve the stochastic Lotka-Volterra model well, is presented.