Certain asymptotic results for the stationary characteristics of semimarkovian random walk with constraint

Xanıyev T., YAZIR T., KESEMEN O., Aliev R.

Automatic Control and Computer Sciences, vol.40, no.1, pp.26-37, 2006 (Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 40 Say: 1
  • Nəşr tarixi: 2006
  • jurnalın adı: Automatic Control and Computer Sciences
  • Jurnalın baxıldığı indekslər: Scopus
  • Səhifə sayı: pp.26-37
  • Açar sözlər: Asymptotic expansion, Discrete interference of events, Ergodic distribution, Erlangian distribution, Ladder variables, Semi-Markovian walk
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In the present study a process (X(t)) of semi-Markovian walk with level constraint s > 0 is investigated. Under extremely weak conditions it is proved that this process is ergodic. Exact formulas are obtained for the first and second moments of the ergodic distribution of the process X(t), in which the random variable ζ1, which describes the discrete interference of events, has third-order Erlangian distribution with parameter λ > 0. Using these results third-order asymptotic expansions for the mathematical expectation and variance of the ergodic distribution of the process X(t) as λ → 0 are obtained. © 2006 by Allerton Press, Inc.