New and refined bounds for expected maxima of fractional Brownian motion

Borovkov, K; Mishura, Y; Novikov, A; Zhitlukhin, M

New and refined bounds for expected maxima of fractional Brownian motion

Borovkov, K Mishura, Y Novikov, A

Zhitlukhin, M

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Publication Type:: Journal Article
Citation:: Statistics and Probability Letters, 2018, 137 pp. 142 - 147
Issue Date:: 2018-06-01

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Field	Value	Language
dc.contributor.author	Borovkov, K	en_US
dc.contributor.author	Mishura, Y	en_US
dc.contributor.author	Novikov, A https://orcid.org/0000-0001-8529-173X	en_US
dc.contributor.author	Zhitlukhin, M	en_US
dc.date.issued	2018-06-01	en_US
dc.identifier.citation	Statistics and Probability Letters, 2018, 137 pp. 142 - 147	en_US
dc.identifier.issn	0167-7152	en_US
dc.identifier.uri	http://hdl.handle.net/10453/130755
dc.description.abstract	© 2018 Elsevier B.V. For the fractional Brownian motion BH with the Hurst parameter value H in (0,1∕2), we derive new upper and lower bounds for the difference between the expectations of the maximum of BH over [0,1] and the maximum of BH over the discrete set of values in−1, i=1,…,n. We use these results to improve our earlier upper bounds for the expectation of the maximum of BH over [0,1] and derive new upper bounds for Pickands’ constant.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP150102758
dc.relation.ispartof	Statistics and Probability Letters	en_US
dc.relation.isbasedon	10.1016/j.spl.2018.01.025	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	New and refined bounds for expected maxima of fractional Brownian motion	en_US
dc.type	Journal Article
utslib.citation.volume	137	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	137	en_US

Abstract:

© 2018 Elsevier B.V. For the fractional Brownian motion BH with the Hurst parameter value H in (0,1∕2), we derive new upper and lower bounds for the difference between the expectations of the maximum of BH over [0,1] and the maximum of BH over the discrete set of values in−1, i=1,…,n. We use these results to improve our earlier upper bounds for the expectation of the maximum of BH over [0,1] and derive new upper bounds for Pickands’ constant.

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http://hdl.handle.net/10453/130755