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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A cascade decomposition theory with applications to Markov and exchangeable cascades
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by Edward C. Waymire and Stanley C. Williams PDF
Trans. Amer. Math. Soc. 348 (1996), 585-632 Request permission


A multiplicative random cascade refers to a positive $T$-martingale in the sense of Kahane on the ultrametric space $T = { \{ 0,1,\dots ,b-1 \} }^{\mathbf {N}}.$ A new approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) non-degeneracy criterion, (ii) dimension spectra of carrying sets, and (iii) divergence of moments criterion. Specific applications are given to cascades generated by Markov and exchangeable processes, as well as to homogeneous independent cascades.
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Additional Information
  • Edward C. Waymire
  • MR Author ID: 180975
  • Email:
  • Stanley C. Williams
  • Email:
  • Received by editor(s): August 18, 1994
  • Additional Notes: The authors would like to thank an anonymous referee for several suggestions, both technical and otherwise, which improved the readability of this paper. This research was partially supported by grants from NSF and NASA
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 585-632
  • MSC (1991): Primary 60G57, 60G30, 60G42; Secondary 60K35, 60D05, 60J10, 60G09
  • DOI:
  • MathSciNet review: 1322959