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The Weak Convergence Theorem for the Distribution of the Maximum of a Gaussian Random Walk and Approximation Formulas for its Moments |
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| Authors: | Fikri Gökpınar Tahir Khaniyev Zulfiyya Mammadova |
| Affiliation: | 1. Department of Statistics, Gazi University, Ankara, Turkey 2. Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey 3. Institute of Cybernetics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan 4. Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey |
| 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. |
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