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Bipower Variation for Gaussian Processes with Stationary Increments

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Ole E. Barndorff-Nielsen ,
José Manuel Corcuera ,
Mark Podolskij  and
Jeannette H. C. Woerner
Ole E. Barndorff-Nielsen*
Affiliation:
University of Aarhus
José Manuel Corcuera*
Affiliation:
University of Barcelona
Mark Podolskij*
Affiliation:
University of Aarhus and CREATES
Jeannette H. C. Woerner*
Affiliation:
University of Göttingen
*
∗Postal address: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark. Email address: oebn@imf.au.dk
∗∗Postal address: Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain. Email address: jmcorcuera@ub.edu
∗∗∗Current address: Department of Mathematics, ETH Zürich, HG G32.2, 8092 Zürich, Switzerland. Email address: mark.podolskij@math.ethz.ch
∗∗∗∗Postal address: Institut für Mathematische Stochastik, Maschmühlenweg 8-10, 37073 Göttingen, Germany. Email address: woerner@math.uni-goettingen.de
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Abstract

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Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing limit laws, due to Nualart, Peccati, and others.

Keywords

Bipower variationcentral limit theoremchaos expansionGaussian processmultiple Wiener–Itô integrals

MSC classification

Secondary: 60G15: Gaussian processes 60F17: Functional limit theorems; invariance principles
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 1 , March 2009 , pp. 132 - 150
Copyright
Copyright © Applied Probability Trust 2009 

References

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