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Boundary non-crossing probabilities for fractional Brownian motion with trend
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 87, no 6, 946-965 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large trend function. As a by-product, we solve a minimization problem related to the norm of the trend function.

Place, publisher, year, edition, pages
2015. Vol. 87, no 6, 946-965 p.
Keyword [en]
boundary crossings, Cameron–Martin–Girsanov theorem, reproducing kernel Hilbert space, large deviation principle, Molchan martingale, fractional Brownian motion
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-103712DOI: 10.1080/17442508.2015.1019882ISI: 000362724700002OAI: oai:DiVA.org:umu-103712DiVA: diva2:814896
Note

Originally published in manuscript form.

Available from: 2015-05-28 Created: 2015-05-28 Last updated: 2017-12-04Bibliographically approved

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