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A time series approach to the study of the simple subcritical Galton–Watson process with immigration

Published online by Cambridge University Press:  01 July 2016

K. N. Venkataraman
K. N. Venkataraman*
Affiliation:
University of Madras
*
∗Postal address: Department of Statistics, University of Madras, Chepauk, Madras 600 005, India.
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Abstract

The principal aim of this paper is to exhibit applications of techniques of time series analysis for establishing limit distribution theorems of statistical relevance on a subcritical Galton–Watson process X with immigration. In this approach the results obtained by Heyde and Seneta, Quine, and Klimko and Nelson are re-established in a more concise form on adopting new methods of proof, which seek to unify these results. In addition, Quenouille-type limit theorems on X are proved leading to the construction of Quenouille-type goodness-of-fit tests for X. It appears that Billingsley's central limit theorem for martingales is appropriate for proving the basic result, Theorem 1.1. This is done on converting the entire problem as a martingale problem through a use of Lemma 2 of Venkataraman (1968).

Keywords

LIMIT THEOREMSGOODNESS OF FIT
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982 , pp. 1 - 20
Copyright
Copyright © Applied Probability Trust 1982 

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