STOCHASTIC FUNCTIONAL POPULATION DYNAMICS WITH JUMPS

Abstract. 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 stochas- tic 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.