A weak law of large numbers for realised covariation in a Hilbert space setting
File(s)
Published version
Author(s)
Benth, Fred Espen
Schroers, Dennis
Veraart, Almut
Type
Journal Article
Abstract
This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated volatility process arising in general mild solutions of Hilbert space-valued stochastic evolution equations in the sense of Da Prato and Zabczyk (2014). We prove a weak law of large numbers for this estimator, where the convergence is uniform on compacts in probability with respect to the Hilbert–Schmidt norm. In addition, we determine convergence rates for common stochastic volatility models in Hilbert spaces.
Date Issued
2022-03-01
Date Acceptance
2021-12-15
Citation
Stochastic Processes and their Applications, 2022, 145, pp.241-268
ISSN
0304-4149
Publisher
Elsevier
Start Page
241
End Page
268
Journal / Book Title
Stochastic Processes and their Applications
Volume
145
Copyright Statement
© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Subjects
Statistics & Probability
0102 Applied Mathematics
0104 Statistics
1502 Banking, Finance and Investment
Publication Status
Published
Date Publish Online
2021-12-24