Chemotaxis stochastic model for two populations

We construct a probabilistic representation of the Cauchy problem weak solution for a system of parabolic equations describing a chemotaxis process in a system of two interacting populations. We derive a stochastic system describing the Keller–Segel type chemotaxis process and the Lotka–Voltera type interatction between two populations and prove existence and uniqueness theorem for its solution. Finally, we show connections between solutions of the stochastic system and the Cauchy problem weak solution of the original PDE system.