Long-time behaviour of a stochastic prey–predator model

Abstract We consider a system of stochastic equations which models the population dynamics of a prey–predator type. We show that the distributions of the solutions of this system are absolutely continuous. We analyse long-time behaviour of densities of the distributions of the solutions. We prove that the densities can converge in L 1 to an invariant density or can converge weakly to a singular measure.