Global solutions and boundedness of stochastic functional Kolmogorov system with infinite delay

This paper investigates the existence and boundedness of the global positive solutions for stochastic Kolmogorov system with infinite delay. We obtain two classes of sufficient conditions to guarantee these properties. These two classes of the conditions show that the system is dominated by deterministic part or stochastic part respectively. By the M-matrix technique, we conveniently compare our results. Finally, a Lotka-Volterra model as a special case is given to illustrate our idea.