Limit theorems for multivariate Brownian semistationary processes and feasible results

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Title: Limit theorems for multivariate Brownian semistationary processes and feasible results
Authors: Passeggeri, R
Veraart, A
Item Type: Journal Article
Abstract: In this paper we introduce the multivariate Brownian semistationary (BSS) process and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general multivariate Gaussian processes with stationary increments, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.
Issue Date: Sep-2019
Date of Acceptance: 3-Apr-2019
DOI: 10.1017/apr.2019.30
ISSN: 0001-8678
Publisher: Cambridge University Press
Start Page: 667
End Page: 716
Journal / Book Title: Advances in Applied Probability
Volume: 51
Issue: 3
Copyright Statement: © Applied Probability Trust 2019. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Multivariate Brownian semistationary process
central limit theorem
law of large numbers
high frequency data
gamma kernel
Wiener chaos
0102 Applied Mathematics
0104 Statistics
Statistics & Probability
Publication Status: Published
Online Publication Date: 2019-09-03
Appears in Collections:Mathematics
Faculty of Natural Sciences

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