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arXiv · 0910.1319

Conditionally monotone independence II: Multiplicative convolutions and infinite divisibility

Takahiro Hasebe
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Abstract

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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Takahiro Hasebe. 2011-03-26. Conditionally monotone independence II: Multiplicative convolutions and infinite divisibility. https://arxiv.org/abs/0910.1319

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