Approximation formulas for the moments of the boundary functional of a Gaussian random walk with positive drift by using Siegmund's formula

GÖKPINAR F., Khaniyev T., Aliyev R.

Communications in Statistics: Simulation and Computation, vol.48, no.9, pp.2679-2688, 2019 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 48 Say: 9
  • Nəşr tarixi: 2019
  • Doi nömrəsi: 10.1080/03610918.2018.1468449
  • jurnalın adı: Communications in Statistics: Simulation and Computation
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.2679-2688
  • Açar sözlər: Boundary functional, Dynkin principle, Gaussian random walk, Ladder height, Meta-modeling, Positive drift, Reimann zeta-function
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

In this study, a boundary functional ((Formula presented.)) are mathematically constructed for a Gaussian random walk (GRW) with positive drift β and first four moments of the functional (Formula presented.) are expressed in terms of ladder variables based on Dynkin Principle. Moreover, approximation formulas for first three moments of ladder height (Formula presented.) are proposed based on the formulas of Siegmund (1979) when β ↓0. Finally, approximation formulas for the first four moments of the boundary functional (Formula presented.) are obtained by using Siegmund formulas and meta modeling, when β ∈[0.1, 3.6].