Vol. 237, No. 2, 2008

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ISSN: 0030-8730
Limit laws for Boolean convolutions

Jiun-Chau Wang

Vol. 237 (2008), No. 2, 349–371
Abstract

We study the distributional behavior for products and sums of Boolean independent random variables in a general infinitesimal triangular array. We show that the limit laws of Boolean convolutions are determined by the limit laws of free convolutions, and vice versa. We further use these results to demonstrate several connections between the limiting distributional behavior of classical convolutions and that of Boolean convolutions. The proof of our results is based on the analytical apparatus developed by Bercovici and Wang for free convolutions.

Keywords
Boolean convolution, limit theorems, infinitesimal arrays
Mathematical Subject Classification 2000
Primary: 46L54, 46L53
Milestones
Received: 30 July 2007
Accepted: 4 June 2008
Published: 1 October 2008
Authors
Jiun-Chau Wang
Department of Mathematics
Indiana University
Bloomington, Indiana 47405
United States