A central limit theorem for martingales and an application to branching processes

D. J. Scott

Stochastic Processes and their Applications, 1978, vol. 6, issue 3, 241-252

Abstract: A functional central limit theorem is obtained for martingales which are not uniformly asymptotically negligible but grow at a geometric rate. The function space is not the usual C[0,1] or D[0,1] but RN, the space of all real sequences and the metric used leads to a non-separable metric space. The main theorem is applied to a martingale obtained from a supercritical Galton-Watson branching process and as simple corollaries the already known central limit theorems for the Harris and Lotka-Nagaev estimators of the mean of the offspring distribution, are obtained.

Date: 1978
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