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2022 Infinite convolutions of probability measures on Polish semigroups
Kouji Yano
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Probab. Surveys 19: 129-159 (2022). DOI: 10.1214/22-PS6

Abstract

This expository paper is intended for a short self-contained introduction to the theory of infinite convolutions of probability measures on Polish semigroups. We give the proofs of the Rees decomposition theorem of completely simple semigroups, the Ellis–Żelazko theorem, the convolution factorization theorem of convolution idempotents, and the convolution factorization theorem of cluster points of infinite convolutions.

Funding Statement

The research of Kouji Yano was supported by JSPS KAKENHI grant no.’s JP19H01791 and JP19K21834 and by JSPS Open Partnership Joint Research Projects grant no. JPJSBP120209921. This research was supported by RIMS and by ISM.

Citation

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Kouji Yano. "Infinite convolutions of probability measures on Polish semigroups." Probab. Surveys 19 129 - 159, 2022. https://doi.org/10.1214/22-PS6

Information

Received: 1 August 2021; Published: 2022
First available in Project Euclid: 25 March 2022

arXiv: 2108.12588
Digital Object Identifier: 10.1214/22-PS6

Subjects:
Primary: 60B15
Secondary: 60F05 , 60G50

Keywords: convolution idempotent , Ellis–Żelazko theorem , infinite convolution , Polish semigroup , Rees decomposition

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Vol.19 • 2022
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