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Stochastic Lotka-Volterra system with infinite delay. (English) Zbl 1205.34103
Summary: This paper investigates a stochastic Lotka-Volterra system with infinite delay, whose initial data comes from an admissible Banach space $$C_r$$. We show that, under a simple hypothesis on the environmental noise, the stochastic Lotka-Volterra system with infinite delay has a unique global positive solution, and this positive solution will be asymptotic bounded. The asymptotic pathwise of the solution is also estimated by the exponential martingale inequality. Finally, two examples with their numerical simulations are provided to illustrate our result.

##### MSC:
 34K50 Stochastic functional-differential equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 92D25 Population dynamics (general)
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##### References:
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