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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Detalles Bibliográficos
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
Descripción
Sumario: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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