STOCHASTIC-MODEL OF AN INTEGRABLE NONLINEAR-SYSTEM

A stochastic model is introduced for a Lotka-Volterra system of a finite number of particles. For the case of an infinite number of particles, the system of 2s + 1 species is described by an integrable dynamical system with s + 1 conserved quantities. A natural extension of the s + 1 conserved quantities is given for the stochastic system of finite particles, which may give a stochastic analogue of the integrable dynamical system.