On the limiting behavior of the characteristic function of the ergodic distribution of the semi-Markov walk with two boundaries

Aliyev R., Khaniyev T.

Mathematical Notes, vol.102, no.3-4, pp.444-454, 2017 (SCI-Expanded) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 102 Say: 3-4
  • Nəşr tarixi: 2017
  • Doi nömrəsi: 10.1134/s0001434617090164
  • jurnalın adı: Mathematical Notes
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.444-454
  • Açar sözlər: characteristic function of the ergodic distribution of the semi-Markov walk, semi-Markov walk
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

The semi-Markov walk (X(t)) with two boundaries at the levels 0 and β > 0 is considered. The characteristic function of the ergodic distribution of the processX(t) is expressed in terms of the characteristics of the boundary functionals N(z) and SN(z), where N(z) is the firstmoment of exit of the random walk {Sn}, n ≥ 1, from the interval (−z, β − z), z ∈ [0, β]. The limiting behavior of the characteristic function of the ergodic distribution of the process Wβ(t) = 2X(t)/β − 1 as β → ∞ is studied for the case in which the components of the walk (ηi) have a two-sided exponential distribution.