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2014 Second quantisation for skew convolution products of measures in Banach spaces
David Applebaum, Jan Neerven
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Electron. J. Probab. 19: 1-17 (2014). DOI: 10.1214/EJP.v19-3031


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.


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David Applebaum. Jan Neerven. "Second quantisation for skew convolution products of measures in Banach spaces." Electron. J. Probab. 19 1 - 17, 2014.


Accepted: 17 January 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1291.60012
MathSciNet: MR3164764
Digital Object Identifier: 10.1214/EJP.v19-3031

Primary: 81S25
Secondary: 47N30 , 60B05 , 60E07 , 60G51 , 60G57 , 60H07 , 60J35

Keywords: infinitely divisible measure , Poisson random measure , Second quantisation , skew convolution family , Wiener-Ito decomposition


Vol.19 • 2014
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