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 identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 9
  • Publication Date: 2019
  • Doi Number: 10.1080/03610918.2018.1468449
  • Journal Name: Communications in Statistics: Simulation and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2679-2688
  • Keywords: Boundary functional, Dynkin principle, Gaussian random walk, Ladder height, Meta-modeling, Positive drift, Reimann zeta-function
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

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].