Applebaum, D.B. and Dooley, A. (2015) A Generalised Gangolli-Levy-Khintchine Formula for Infinitely Divisible Measures and Levy Processes on Semi-Simple Lie Groups and Symmetric Spaces. Annales d'Institut Henri Poincare: Probability and Statistics, 51 (2). pp. 599-619. ISSN 0246-0203
Abstract
In 1964 R.Gangolli published a Levy-Khintchine type formula which characterised K bi-invariant infinitely divisible probability measures on a symmetric space G=K. His main tool was Harish-Chandra's spherical functions which he used to construct a generalisation of the Fourier transform of a measure. In this paper we use generalised spherical functions (or Eisenstein integrals) and extensions of these which we construct using representation theory to obtain such a characterisation for arbitrary infinitely divisible probability measures on a non-compact symmetric space. We consider the example of hyperbolic space in some detail.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Institut Henri Poincaré. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Feb 2016 10:55 |
Last Modified: | 12 Mar 2016 23:43 |
Published Version: | http://dx.doi.org/10.1214/13-AIHP570 |
Status: | Published |
Publisher: | Institut Henri Poincaré |
Refereed: | Yes |
Identification Number: | 10.1214/13-AIHP570 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92727 |