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Weak convergence of an autoregressive process used in modeling population growth

Published online by Cambridge University Press:  14 July 2016

W. G. Cumberland  and
Z. M. Sykes
W. G. Cumberland*
Affiliation:
University of California at Los Angeles
Z. M. Sykes*
Affiliation:
The Johns Hopkins University
*
∗ Postal address: School of Public Health, University of California, Los Angeles, CA 90024, U.S.A.
∗∗ Postal address: Department of Population Dynamics, The Johns Hopkins University, Baltimore, MD 21205, U.S.A.
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Abstract

Under simple limiting conditions a first-order autoregressive process is shown to converge weakly to an Ornstein-Uhlenbeck process. The result is discussed in the context of modeling vital rates for biological populations in random environments.

Keywords

MODELING VITAL RATESORNSTEIN–UHLENBECK PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 450 - 455
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported by a training grant (5-TO1-HN109), by a research career program award (5-KO4-Hd70404), and by a research grant (1-RO1-HD8959), all from the National Institute of Child Health and Human Development.

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