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arXiv:math/0305200 [math.PR]AbstractReferencesReviewsResources

On the uniqueness of the branching parameter for a random cascade measure

G. Molchan

Published 2003-05-14Version 1

An independent random cascade measure is specified by a random generator, a vector of dimension c with non-negative components. The dimension c is called the branching cascade parameter. It is shown under certain restrictions that, if this measure has two generators with a.s. positive components, and the ratio ln c_1/ln c_2 for their branching parameters is an irrational number, then this measure is a Lebesgue measure. In other words, when c is a power of an integer number p and the p is minimal for c, then a cascade measure that has the property of intermittency specifies p uniquely.

Comments: 18 pages, no figures
Categories: math.PR, math-ph, math.MP
Subjects: 60G57, 60G18
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