Bounds for expected maxima of Gaussian processes and their discrete approximations

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

Bounds for expected maxima of Gaussian processes and their discrete approximations

Borovkov, K Mishura, Y Novikov, A

Zhitlukhin, M

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Publication Type:: Journal Article
Citation:: Stochastics, 2017, 89 (1), pp. 21 - 37
Issue Date:: 2017-01-02

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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	2017-01-02	en_US
dc.identifier.citation	Stochastics, 2017, 89 (1), pp. 21 - 37	en_US
dc.identifier.issn	1744-2508	en_US
dc.identifier.uri	http://hdl.handle.net/10453/42036
dc.description.abstract	© 2015 Taylor & Francis. The paper deals with the expected maxima of continuous Gaussian processes X = (Xt)t≥0 that are Hölder continuous in L2-norm and/or satisfy the opposite inequality for the L2-norms of their increments. Examples of such processes include the fractional Brownian motion and some of its “relatives” (of which several examples are given in the paper). We establish upper and lower bounds for Emax≤t≤1 Xt and investigate the rate of convergence to that quantity of its discrete approximation Emax0≤i≤n Xi/n. Some further properties of these two maxima are established in the special case of the fractional Brownian motion.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP150102758
dc.relation.ispartof	Stochastics	en_US
dc.relation.isbasedon	10.1080/17442508.2015.1126282	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Bounds for expected maxima of Gaussian processes and their discrete approximations	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	89	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	15 Commerce, Management, Tourism and Services	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.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	89	en_US

Abstract:

© 2015 Taylor & Francis. The paper deals with the expected maxima of continuous Gaussian processes X = (Xt)t≥0 that are Hölder continuous in L2-norm and/or satisfy the opposite inequality for the L2-norms of their increments. Examples of such processes include the fractional Brownian motion and some of its “relatives” (of which several examples are given in the paper). We establish upper and lower bounds for Emax≤t≤1 Xt and investigate the rate of convergence to that quantity of its discrete approximation Emax0≤i≤n Xi/n. Some further properties of these two maxima are established in the special case of the fractional Brownian motion.

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http://hdl.handle.net/10453/42036