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Second quantisation for skew convolution products of measures in Banach spaces

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Second quantisation for skew convolution products of measures in Banach spaces
2.	Creator	Author's name, affiliation, country	David Applebaum; University of Sheffield; United Kingdom
2.	Creator	Author's name, affiliation, country	Jan van Neerven; Delft University of Technology; Netherlands
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Second quantisation, skew convolution family, infinitely divisible measure, Wiener-Ito decomposition, Poisson random measure
3.	Subject	Subject classification	Primary 81S25, Secondary 47N30, 60B05, 60E07, 60G51, 60G57, 60J35, 60H07
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Netherlands Organisation for Scientific Research (NWO)
7.	Date	(YYYY-MM-DD)	2014-01-17
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/3031
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3031
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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