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The Functional Equation of the Smoothing Transform

ANNALS OF PROBABILITY, no. 5 (2012): 2069-2105

Cited by: 55|Views5

Abstract

Given a sequence T = (T-i)(i >= 1) of nonnegative random variables, a function f on the positive halfline can be transformed to E Pi(i >= 1) f (tT(i)). We study the fixed points of this transform within the class of decreasing functions. By exploiting the intimate relationship with general branching processes, a full description of the se...More

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