Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance

Xanıyev T., YAZIR T., Aliyev R., KOKANGÜL A.

Statistics and Probability Letters, vol.78, no.6, pp.785-793, 2008 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 78 Say: 6
  • Nəşr tarixi: 2008
  • Doi nömrəsi: 10.1016/j.spl.2007.09.045
  • jurnalın adı: Statistics and Probability Letters
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.785-793
  • Açar sözlər: Asymptotic expansion, Discrete interference of chance, Ergodic distribution, First jump, Ladder variable, Random walk
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In this paper, a semi-Markovian random walk process (X (t)) with a discrete interference of chance is constructed and the ergodicity of this process is discussed. Some exact formulas for the first- and second-order moments of the ergodic distribution of the process X (t) are obtained, when the random variable ζ1 has an exponential distribution with the parameter λ > 0. Here ζ1 expresses the quantity of a discrete interference of chance. Based on these results, the third-order asymptotic expansions for mathematical expectation and variance of the ergodic distribution of the process X (t) are derived, when λ → 0. © 2007 Elsevier B.V. All rights reserved.