Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1152230 | Statistics & Probability Letters | 2012 | 7 Pages |
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
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Jeff T. Terpstra, Tamer Elbayoumi,