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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Gokpmar F., Khaniyev T., Mammadova Z.

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, vol.15, no.2, pp.333-347, 2013 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 15 Issue: 2
• Publication Date: 2013
• Doi Number: 10.1007/s11009-011-9240-0
• Journal Name: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.333-347
• Karadeniz Technical University Affiliated: Yes

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.