Extreme values of Markov population processes

A. D. Barbour

Stochastic Processes and their Applications, 1983, vol. 14, issue 3, 297-313

Abstract: In contrast to the classical theory of partial sums of independent and identically distributed random variables, the maximum value taken by a component of a Markov population process xN is typically largely determined by the variation in its mean, rather than by stochastic fluctuation. A closer approximation to its distribution is found by considering the supremum of V(t) - N c(t) for a suitable centred Gaussian process V, where c incorporates the effect of the variation in the mean of xN. Under appropriate conditions, it is shown that this has a distribution which is normally distributed, to within an error of order N- log N, and expressions for the mean and variance of the approximating distribution are derived.

Keywords: Markov; population; process; maximum; of; epidemic; extreme; value; higher; order; limit; theorems (search for similar items in EconPapers)
Date: 1983
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