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Some convergence theorems on a supercritical Galton-Watson process

Authors:	P Koteeswaran K Nanthi K Suresh Chandra

Institution:	(1) University of Madras, Madras;(2) Presidency College, Madras

Abstract:	Summary LetX=(X _n; n≧0,X ₀=1) be a supercritical Galton-Watson process. The limiting distribution of $\left( {\left( {\sum\limits_{n = 0}^N {X_n } } \right)^{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {\sum\limits_{n = 0}^N {X_{n + r} } - \hat m^r \sum\limits_{n = 0}^N {X_n } } \right);r = 2,3, \ldots ,T} \right)$ ) where $\hat m$ is the m.l.e. of the offspring mean, is derived. As an application of this result, some limit theorems leading ultimately to a parameter free result of statistical interest, are also established.

Keywords:	Supercritical Galton-Watson process asymptotic goodness of fit tests
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