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Extreme values of Markov population processes

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  • Barbour, A. D.

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.

Suggested Citation

  • Barbour, A. D., 1983. "Extreme values of Markov population processes," Stochastic Processes and their Applications, Elsevier, vol. 14(3), pages 297-313, March.
    • Handle: RePEc:eee:spapps:v:14:y:1983:i:3:p:297-313
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