The Weak Convergence Theorem for the Distribution of the Maximum of a Gaussian Random Walk and Approximation Formulas for its Moments

Fikri Gökpınar (), Tahir Khaniyev and Zulfiyya Mammadova
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Fikri Gökpınar: Gazi University
Tahir Khaniyev: TOBB University of Economics and Technology
Zulfiyya Mammadova: Karadeniz Technical University

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 2, 333-347

Abstract: Abstract In this study, asymptotic expansions of the moments of the maximum (M(β)) of Gaussian random walk with negative drift ( − β), β > 0, are established by using Bell Polynomials. In addition, the weak convergence theorem for the distribution of the random variable Y(β) ≡ 2 β M(β) 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 β ∈ (0.5, 3.2] using meta-modeling.

Keywords: Gaussian random walk; Maximum of random walk; Weak convergence; Moments; Bell polynomial; Asymptotic expansion; Approximation formula; Meta-modeling; Primary 60G50; Secondary 60F05, 60G15 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9240-0

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