Stochastic reaction-diffusion system modeling predator-prey interactions with prey-taxis and noises.

In this paper, we are concerned with a new stochastic system of nonlinear partial differential equations modeling the Lotka-Volterra interactions of predators and preys in the presence of prey-taxis, spatial diffusion, and noises. The spatial and temporal variations of the predator's velocity are determined by the prey gradient. In the first part, we derive a macroscopic model from stochastic kinetic equations by using the micro-macro decomposition method.