Central Limit Analogues for Markov Population Processes

It is shown in this paper that several birth-death-type models (univariate as well as multivariate) can be approximated by Ornstein-Uhlenbeck processes as certain parameters become large. Such approximations are valuable whenever the Kolmogorov differential equation cannot be solved in closed form.

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1973-01, Vol.35 (1), p.1-23
Main Authors: McNeil, Donald R., Schach, Siegfried
Format: Article
Language:English
Subjects:
Approximation
birth and death processes
convergence of markov processes
Determinism
markov population models
Markov processes
Mortality
Ornstein Uhlenbeck process
ornstein‐uhlenbeck processes
Perceptron convergence procedure
Population growth
Population size
Stochastic processes
Transition probabilities
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Summary:It is shown in this paper that several birth-death-type models (univariate as well as multivariate) can be approximated by Ornstein-Uhlenbeck processes as certain parameters become large. Such approximations are valuable whenever the Kolmogorov differential equation cannot be solved in closed form.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1973.tb00928.x