Limit theorems for power variations of ambit fields driven by white noise

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Title: Limit theorems for power variations of ambit fields driven by white noise
Authors: Pakkanen, MS
Item Type: Journal Article
Abstract: We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power variations converge to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This result holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asymptotic behavior. Our second result is a stable central limit theorem for thinned power variations. © 2014 Elsevier B.V. All rights reserved.
Issue Date: 22-Jan-2014
Date of Acceptance: 15-Jan-2014
ISSN: 0304-4149
Publisher: Elsevier
Start Page: 1942
End Page: 1973
Journal / Book Title: Stochastic Processes and Their Applications
Volume: 124
Issue: 5
Copyright Statement: © 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Publication Status: Published
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences

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