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Permutation invariant functionals of Lévy processes


Authors: F. Baumgartner and S. Geiss
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 60G51; Secondary 37A05, 20B99, 20Bxx, 22D40
DOI: https://doi.org/10.1090/tran/7001
Published electronically: May 30, 2017
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Abstract: We study natural invariance properties of functionals defined on Lévy processes and show that they can be described by a simplified structure of the deterministic chaos kernels in Itô's chaos expansion. These structural properties of the kernels relate intrinsically to a measurability with respect to invariant $ \sigma $-algebras. This makes it possible to apply deterministic functions to invariant functionals on Lévy processes while keeping the simplified structure of the kernels. This stability is crucial for applications. Examples are given as well.


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Additional Information

F. Baumgartner
Affiliation: Department of Mathematics, University of Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria
Email: florian.baumgartner@uibk.ac.at

S. Geiss
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland
Email: stefan.geiss@jyu.fi

DOI: https://doi.org/10.1090/tran/7001
Received by editor(s): November 21, 2014
Received by editor(s) in revised form: January 29, 2016
Published electronically: May 30, 2017
Article copyright: © Copyright 2017 American Mathematical Society