A central limit theorem for age- and density-dependent population processes

Frank J. S. Wang

Stochastic Processes and their Applications, 1977, vol. 5, issue 2, 173-193

Abstract: Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density PA(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence PA(t) would converge to the solution P(t) of our integral equation in the sense that . In this paper, we obtain a "central limit theorem" for the random element [radical sign]A(PA(t)-P(t)). We prove that under appropriate conditions [radical sign]A(PA(t)-P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)

Keywords: population; process; Gaussaian; process; Skorohod; topology; partial; differential; central; limit; theorem; resolvent; kernel; tightness (search for similar items in EconPapers)
Date: 1977
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