Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/7685
Title: The Weak Convergence Theorem for the Distribution of the Maximum of a Gaussian Random Walk and Approximation Formulas for its Moments
Authors: Gökmar, Fikri
Khaniyev, Tahir
Mammadova, Zulfiyya
Keywords: Gaussian random walk
Maximum of random walk
Weak convergence
Moments
Bell polynomial
Asymptotic expansion
Approximation formula
Meta-modeling
Issue Date: 2013
Publisher: Springer
Abstract: In this study, asymptotic expansions of the moments of the maximum (M(beta)) of Gaussian random walk with negative drift ( -aEuro parts per thousand beta), beta > 0, are established by using Bell Polynomials. In addition, the weak convergence theorem for the distribution of the random variable Y(beta) a parts per thousand aEuro parts per thousand 2 beta M(beta) is proved, and the explicit form of the limit distribution is derived. Moreover, the approximation formulas for the first four moments of the maximum of a Gaussian random walk are obtained for the parameter beta aaEuro parts per thousand(0.5, 3.2] using meta-modeling.
URI: https://doi.org/10.1007/s11009-011-9240-0
https://hdl.handle.net/20.500.11851/7685
ISSN: 1387-5841
1573-7713
Appears in Collections:Endüstri Mühendisliği Bölümü / Department of Industrial Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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