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Independent random cascades on Galton-Watson trees
Author(s):
Gregory
A.
Burd;
Edward
C.
Waymire
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2753-2761.
MSC (2000):
Primary 60G57, 60G30, 60G42;
Secondary 60K35
Posted:
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.
References:
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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
Email:
burd@math.washington.edu, gburd@marvell.com
Edward
C.
Waymire
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605
Email:
waymire@math.orst.edu
DOI:
10.1090/S0002-9939-00-05279-5
PII:
S 0002-9939(00)05279-5
Received by editor(s):
May 14, 1998
Received by editor(s) in revised form:
October 8, 1998
Posted:
March 1, 2000
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
2000,
American Mathematical Society
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