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When Knowing Early Matters: Gossip, Percolation and Nash Equilibria Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Limit Theorems for Functionals of Higher Order Differences of Brownian Semi-Stationary Processes

Authors : Ole E. Barndorff-Nielsen, José Manuel Corcuera, Mark Podolskij

Published in: Prokhorov and Contemporary Probability Theory

Publisher: Springer Berlin Heidelberg

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Abstract

We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work [8] we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the smoothness parameter of a Brownian semi-stationary process, and the parameter values which appear in typical applications, e.g. in modeling turbulent flows in physics, were excluded. The main goal of the current paper is the derivation of the asymptotic theory for the whole range of the smoothness parameter by means of using second order differences. We present the law of large numbers for the multipower variation of the second order differences of Brownian semi-stationary processes and show the associated central limit theorem. Finally, we demonstrate some estimation methods for the smoothness parameter of a Brownian semi-stationary process as an application of our probabilistic results.

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previous chapter The Shape of Asymptotic Dependence
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Metadata
Title
Limit Theorems for Functionals of Higher Order Differences of Brownian Semi-Stationary Processes
Authors
Ole E. Barndorff-Nielsen
José Manuel Corcuera
Mark Podolskij
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Prokhorov and Contemporary Probability Theory

Print ISBN: 978-3-642-33548-8

Electronic ISBN: 978-3-642-33549-5

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-33549-5_4