Derivative of the expected supremum of fractional Brownian motion at [Formula: see text]

The H-derivative of the expected supremum of fractional Brownian motion [Formula: see text] with drift [Formula: see text] over time interval [0, T] [Formula: see text] at [Formula: see text] is found. This formula depends on the quantity [Formula: see text] , which has a probabilistic form. The num...

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Autores principales: Bisewski, Krzysztof, Dȩbicki, Krzysztof, Rolski, Tomasz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9534823/
https://www.ncbi.nlm.nih.gov/pubmed/36213862
http://dx.doi.org/10.1007/s11134-022-09859-3
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author Bisewski, Krzysztof
Dȩbicki, Krzysztof
Rolski, Tomasz
author_facet Bisewski, Krzysztof
Dȩbicki, Krzysztof
Rolski, Tomasz
author_sort Bisewski, Krzysztof
collection PubMed
description The H-derivative of the expected supremum of fractional Brownian motion [Formula: see text] with drift [Formula: see text] over time interval [0, T] [Formula: see text] at [Formula: see text] is found. This formula depends on the quantity [Formula: see text] , which has a probabilistic form. The numerical value of [Formula: see text] is unknown; however, Monte Carlo experiments suggest [Formula: see text] . As a by-product we establish a weak limit theorem in C[0, 1] for the fractional Brownian bridge, as [Formula: see text] .
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spelling pubmed-95348232022-10-07 Derivative of the expected supremum of fractional Brownian motion at [Formula: see text] Bisewski, Krzysztof Dȩbicki, Krzysztof Rolski, Tomasz Queueing Syst Article The H-derivative of the expected supremum of fractional Brownian motion [Formula: see text] with drift [Formula: see text] over time interval [0, T] [Formula: see text] at [Formula: see text] is found. This formula depends on the quantity [Formula: see text] , which has a probabilistic form. The numerical value of [Formula: see text] is unknown; however, Monte Carlo experiments suggest [Formula: see text] . As a by-product we establish a weak limit theorem in C[0, 1] for the fractional Brownian bridge, as [Formula: see text] . Springer US 2022-08-30 2022 /pmc/articles/PMC9534823/ /pubmed/36213862 http://dx.doi.org/10.1007/s11134-022-09859-3 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Bisewski, Krzysztof
Dȩbicki, Krzysztof
Rolski, Tomasz
Derivative of the expected supremum of fractional Brownian motion at [Formula: see text]
title Derivative of the expected supremum of fractional Brownian motion at [Formula: see text]
title_full Derivative of the expected supremum of fractional Brownian motion at [Formula: see text]
title_fullStr Derivative of the expected supremum of fractional Brownian motion at [Formula: see text]
title_full_unstemmed Derivative of the expected supremum of fractional Brownian motion at [Formula: see text]
title_short Derivative of the expected supremum of fractional Brownian motion at [Formula: see text]
title_sort derivative of the expected supremum of fractional brownian motion at [formula: see text]
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9534823/
https://www.ncbi.nlm.nih.gov/pubmed/36213862
http://dx.doi.org/10.1007/s11134-022-09859-3
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