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Stochastic functional population dynamics with jumps. (English) Zbl 1373.60117
Summary: In this paper we use a class of stochastic functional Kolmogorov-type model with jumps to describe the evolutions of population dynamics. By constructing a special Lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we discuss the asymptotic pathwise estimation of such a model.
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J75 Jump processes (MSC2010)
92D15 Problems related to evolution
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