Conditionally monotone independence II: Multiplicative convolutions and infinite divisibility

Details Conditionally monotone independence II: Multiplicative convolutions and infinite divisibility Conditionally monotone independence II: Multiplicative convolutions and infinite divisibility

2009-10-07

arxiv.org/abs/0910.1319v3

Mathematics

Operator Algebras

17 pages; introductory presentations changed; accepted for publication in Complex Analysis and Operator Theory

Scientific paper

We study the multiplicative convolution for c-monotone independence. This convolution unifies the monotone, Boolean and orthogonal multiplicative convolutions. We characterize convolution semigroups for the c-monotone multiplicative convolution on the unit circle. We also prove that an infinitely divisible distribution can always be embedded in a convolution semigroup. We furthermore discuss the (non)-uniqueness of such embeddings including the monotone case. Finally connections to the multiplicative Boolean convolution are discussed.

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