Derivative of the expected supremum of fractional Brownian motion at H=1
Details
Serval ID
serval:BIB_B91907DA9E91
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Derivative of the expected supremum of fractional Brownian motion at H=1
Journal
Queueing systems
ISSN
0257-0130 (Print)
ISSN-L
0257-0130
Publication state
Published
Issued date
2022
Peer-reviewed
Oui
Volume
102
Number
1-2
Pages
53-68
Language
english
Notes
Publication types: Journal Article
Publication Status: ppublish
Publication Status: ppublish
Abstract
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 .
Keywords
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
Yes
Funding(s)
Swiss National Science Foundation / Projects / 200021-196888
Create date
03/09/2022 12:33
Last modification date
12/09/2023 5:55
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