Permutation invariant functionals of Lévy processes
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- by F. Baumgartner and S. Geiss PDF
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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.References
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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
- MR Author ID: 248903
- Email: stefan.geiss@jyu.fi
- Received by editor(s): November 21, 2014
- Received by editor(s) in revised form: January 29, 2016
- Published electronically: May 30, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 8607-8641
- MSC (2010): Primary 60G51; Secondary 37A05, 20B99, 20Bxx, 22D40
- DOI: https://doi.org/10.1090/tran/7001
- MathSciNet review: 3710637