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Independent random cascades on Galton-Watson trees

Authors: Gregory A. Burd and Edward C. Waymire
Journal: Proc. Amer. Math. Soc. 128 (2000), 2753-2761
MSC (2000): Primary 60G57, 60G30, 60G42; Secondary 60K35
Published electronically: March 1, 2000
MathSciNet review: 1657774
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Abstract: Consider an independent random cascade acting on the positive Borel measures defined on the boundary of a Galton-Watson tree. Assuming an offspring distribution with finite moments of all orders, J. Peyrière computed the fine scale structure of an independent random cascade on Galton-Watson trees. In this paper we use developments in the cascade theory to relax and clarify the moment assumptions on the offspring distribution. Moreover a larger class of initial measures is covered and, as a result, it is shown that it is the Hölder exponent of the initial measure which is the critical parameter in the Peyrière theory.

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Additional Information

Gregory A. Burd
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Address at time of publication: Marvell Semiconductor, Inc., 645 Almanor Avenue, Sunnyvale, California 94086

Edward C. Waymire
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605

Received by editor(s): May 14, 1998
Received by editor(s) in revised form: October 8, 1998
Published electronically: March 1, 2000
Communicated by: Stanley Sawyer
Article copyright: © Copyright 2000 American Mathematical Society

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