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

GÖKPINAR F., Xanıyev T., Mammadova Z.

Methodology and Computing in Applied Probability, vol.15, no.2, pp.333-347, 2013 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 15 Say: 2
  • Nəşr tarixi: 2013
  • Doi nömrəsi: 10.1007/s11009-011-9240-0
  • jurnalın adı: Methodology and Computing in Applied Probability
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.333-347
  • Açar sözlər: Approximation formula, Asymptotic expansion, Bell polynomial, Gaussian random walk, Maximum of random walk, Meta-modeling, Moments, Weak convergence
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

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) ≡ 2βM(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. © 2011 Springer Science+Business Media, LLC.