Imperial College London
Alternate

ProfessorAlmutVeraart

Faculty of Natural Sciences, Department of Mathematics

Head of the Statistics Section, Professor of Statistics
 
 
 
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Contact

 

+44 (0)20 7594 8545a.veraart Website

 
 
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Location

 

551Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Benth:2022:10.1016/j.spa.2021.12.011,
author = {Benth, FE and Schroers, D and Veraart, A},
doi = {10.1016/j.spa.2021.12.011},
journal = {Stochastic Processes and their Applications},
pages = {241--268},
title = {A weak law of large numbers for realised covariation  in a Hilbert space setting},
url = {http://dx.doi.org/10.1016/j.spa.2021.12.011},
volume = {145},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Benth,FE
AU  - Schroers,D
AU  - Veraart,A
DO  - 10.1016/j.spa.2021.12.011
EP  - 268
PY  - 2022///
SN  - 0304-4149
SP  - 241
TI  - A weak law of large numbers for realised covariation  in a Hilbert space setting
T2  - Stochastic Processes and their Applications
UR  - http://dx.doi.org/10.1016/j.spa.2021.12.011
UR  - http://hdl.handle.net/10044/1/93471
VL  - 145
ER  -
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