Stochastic Kolmogorov-Type Population Dynamics with Infinite Distributed Delays

This paper shows that different environmental noise structures have different effects on population systems. Under two classes of environmental noise perturbations, this paper establishes existence-and-uniqueness theorems of the global positive solution to the stochastic Kolmogorov-type system with infinite distributed delays. As the desired results to population dynamics, this paper also examines asymptotic boundedness, including the moment boundedness and the moment average boundedness in time. To illustrate our idea more clearly, we also discuss a scalar example with mixed delays and a n-dimensional stochastic Lotka-Volterra system with mixed delays.