A general decomposition theory for random cascades

Waymire, Edward C.; Williams, Stanley C.

doi:10.1090/S0273-0979-1994-00521-X

A general decomposition theory for random cascades
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by Edward C. Waymire and Stanley C. Williams PDF

Bull. Amer. Math. Soc. 31 (1994), 216-222 Request permission

Abstract:

This announcement describes a probabilistic approach to cascades which, in addition to providing an entirely probabilistic proof of the Kahane-Peyrière theorem for independent cascades, readily applies to general dependent cascades. Moreover, this unifies various seemingly disparate cascade decompositions, including Kahane’s T-martingale decomposition and dimension disintegration.

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A cascade decomposition theory with applications to Markov and exchangeable cascades