Monotone and Boolean Convolutions for Non-compactly Supported Probability Measures

Details Monotone and Boolean Convolutions for Non-compactly Supported Probability Measures Monotone and Boolean Convolutions for Non-compactly Supported Probability Measures

2007-03-14

arxiv.org/abs/math/0703408v3

Indiana Univ. Math. J. 58 No. 3 (2009), 1151-1186

Mathematics

Functional Analysis

32 pages, new Lemma 2.1

Scientific paper

The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean convolution of probability measures on the positive half-line is proposed. Unlike Bercovici's multiplicative boolean convolution it is always defined, but it turns out to be neither commutative nor associative. Finally some relations between free, monotone, and boolean convolutions are discussed.

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