Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/3748
Title: Bounds on the expected value of maximum loss of fractional Brownian motion
Authors: Acar, Ceren Vardar
Bulut, Hatice
Keywords: Cholesky decomposition
Hurst parameter
Fractional Brownian motion
Maximum loss
Sudakov-Fernique inequality
Issue Date: Sep-2015
Publisher: Elsevier B.V.
Source: Vardar-Acar, C., & Bulut, H. (2015). Bounds on the expected value of maximum loss of fractional Brownian motion. Statistics & Probability Letters, 104, 117-122.
Abstract: It has been theoretically proven through present study that the expected value of maximum loss of fractional Brownian motion up to fixed time t with Hurst parameter [1/2, 1) is bounded above by tH??/2 and below by tH/2. These new bounds provide improvement on those bounds which have been previously derived in the literature. In order to search for closer bounds, numerical study is also performed through discretization method and multivariate Gaussian variables have been examined. The simulated values of the expected value of maximum loss of fractional Brownian motion have been provided through the use of Cholesky decomposition. As a consequence of the simulation study, it has been observed that as the Hurst parameter increases, the values of the expected maximum loss of fractional Brownian motion decreases.
URI: https://doi.org/10.1016/j.spl.2015.05.001
https://hdl.handle.net/20.500.11851/3748
ISSN: 0167-7152
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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