A stochastic model for the Lotka–Volterra system with cross-diffusion

We propose two approaches that allow to construct a probabilistic representation of a generalized solution of the Cauchy problem for a system of quasilinear parabolic equations. The system under consideration presents a population dynamics model for a prey-predator population. We construct two types of stochastic problem associated with this parabolic system that give the way to derive the required probabilistic representation.