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

Gokpmar F., Khaniyev T., Mammadova Z.

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


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.