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Recent investigations involving stochastic population models

Published online by Cambridge University Press:  01 July 2016

M. S. Bartlett
M. S. Bartlett*
Affiliation:
Emeritus Professor of Biomathematics, University of Oxford
*
∗Postal address: Priory Orchard, Priory Avenue, Totnes, Devon TQ9 5HR, U.K.
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Abstract

After some introductory general remarks on recent investigations involving population models, two broad classes of stochastic model are discussed further, viz. spatial nearest-neighbour lattice models and doubly stochastic models.

In Section 1 of the paper, the first type of model is considered primarily for its relevance to recent work by the author and others affecting the practical design and analysis of replicated field experiments.

In Section 2, doubly stochastic processes are discussed more theoretically, particularly models investigated recently by the author involving infinitesimal transition operators in continuous time linear in the (variable) parameters.

Some new numerical results on extinction and other ‘absorption' probabilities are presented; these are intended to throw further light on the extent to which the assumption of ‘white-noise' variability of the parameters can be a useful approximation to more realistic models.

Keywords

NEAREST NEIGHBOURPAPADAKIS METHODDOUBLY STOCHASTIC PROCESSESWHITE NOISESWITCHING MODELSEXTINCTION PROBABILITIESEPIDEMIC SIZE
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 3 , September 1984 , pp. 449 - 470
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

This paper was originally presented as a keynote address at the ORSA/TIMS Special Interest Meeting on Applied Probability in Biology and Engineering, University of Kentucky, Lexington, 18–20 July 1983.

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