A law of large numbers result for a bifurcating process with an infinite moving average representation

Jeff T. Terpstra and Tamer Elbayoumi

Statistics & Probability Letters, 2012, vol. 82, issue 1, 123-129

Abstract: This paper derives a law of large numbers theorem for bifurcating processes defined on a perfect binary tree. This theorem can be viewed as a generalization of some results that have already appeared in the literature. For instance, all that is required of the bifurcating process is an infinite moving average representation with geometrically decaying coefficients and a finite moment assumption. In addition, the summands are assumed to belong to a flexible class of functions that satisfy a generalized Lipschitz type condition. These two criteria allow for an expansive range of applicability. Two examples are given as corollaries to the theorem.

Keywords: Bifurcating process; Binary tree; Covariance inequality; Geometric decay; Law of large numbers (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.09.012

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