Large deviations of Shepp statistics for fractional Brownian motion

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Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Large deviations of Shepp statistics for fractional Brownian motion
Journal
Statistics & Probability Letters
Author(s)
Hashorva E., Tan Z.
ISSN
0167-7152 (Print)
Publication state
Published
Issued date
2013
Peer-reviewed
Oui
Volume
83
Number
10
Pages
2242-2247
Language
english
Abstract
Define the incremental fractional Brownian field Z(H)(tau, S) = B-H (S+tau) By (S), H E (0, 1), where B-H(s) is a standard fractional Brownian motion with Hurst index H is an element of (0, 1). In this paper we derive the exact asymptotic behaviour of the maximum M-H (T) = max((tau,s)is an element of[0,1]x[0,T]) Z(H(tau, S)) for any H is an element of (0,1/2) complimenting thus the result of Zholud (2008) which establishes the exact tail asymptotic behaviour of M-1/2 (T).
Keywords
Shepp statistics, Scan statistics, Exact asymptotics, Extremes, Fractional Brownian motion
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Create date
12/06/2013 11:07
Last modification date
20/08/2019 15:23
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