Applebaum, D. and Neerven, J. (2016) Second quantisation for skew convolution products of measures in Banach spaces. Electronic Journal of Probability, 19. 11. ISSN 1083-6489
Abstract
We study measures in Banach space which arise as the skew convolution product of two other measures where the convolution is deformed by a skew map. This is the structure that underlies both the theory of Mehler semigroups and operator self-decomposable measures. We show how that given such a set-up the skew map can be lifted to an operator that acts at the level of function spaces and demonstrate that this is an example of the well known functorial procedure of second quantisation. We give particular emphasis to the case where the product measure is infinitely divisible and study the second quantisation process in some detail using chaos expansions when this is either Gaussian or is generated by a Poisson random measure.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 The Author(s). |
Keywords: | Skew convolution product; second quantisation; Ornstein-Uhlenbeck semigroup; Poisson random measure |
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: | 09 Mar 2020 14:00 |
Last Modified: | 09 Mar 2020 14:18 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/ejp.v19-3031 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:156707 |