Derivative of the expected supremum of fractional Brownian motion at H=1
Détails
Etat: Public
Version: Final published version
Licence: CC BY 4.0
ID Serval
serval:BIB_B91907DA9E91
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Derivative of the expected supremum of fractional Brownian motion at H=1
Périodique
Queueing systems
ISSN
0257-0130 (Print)
ISSN-L
0257-0130
Statut éditorial
Publié
Date de publication
2022
Peer-reviewed
Oui
Volume
102
Numéro
1-2
Pages
53-68
Langue
anglais
Notes
Publication types: Journal Article
Publication Status: ppublish
Publication Status: ppublish
Résumé
The H-derivative of the expected supremum of fractional Brownian motion with drift over time interval [0, T] <DispFormula xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:xlink="http://www.w3.org/1999/xlink"/>
at is found. This formula depends on the quantity , which has a probabilistic form. The numerical value of is unknown; however, Monte Carlo experiments suggest . As a by-product we establish a weak limit theorem in C[0, 1] for the fractional Brownian bridge, as .
xmlns:xlink="http://www.w3.org/1999/xlink"/>
at is found. This formula depends on the quantity , which has a probabilistic form. The numerical value of is unknown; however, Monte Carlo experiments suggest . As a by-product we establish a weak limit theorem in C[0, 1] for the fractional Brownian bridge, as .
Mots-clé
Computational Theory and Mathematics, Management Science and Operations Research, Computer Science Applications, H-derivative, expected supremum, fractional Brownian motion
Pubmed
Web of science
Open Access
Oui
Financement(s)
Fonds national suisse / Projets / 200021-196888
Création de la notice
03/09/2022 12:33
Dernière modification de la notice
12/09/2023 5:55
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