Weak convergence theorem for ergodic distribution of stochastic processes with discrete interference of chance and generalized reflecting barrier

Aliyev R., Xanıyev T., Gever B.

Theory of Probability and its Applications, vol.60, no.3, pp.502-513, 2016 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 60 Say: 3
  • Nəşr tarixi: 2016
  • Doi nömrəsi: 10.1137/s0040585x97t987806
  • jurnalın adı: Theory of Probability and its Applications
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.502-513
  • Açar sözlər: Ergodic distribution, Ladder variables, Reflecting barrier, Residual waiting time, Stochastic process with a discrete interference of chance
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In this paper, a stochastic process with discrete interference of chance and generalized reflecting barrier (X (t)) is constructed and the ergodicity of this process is proved. Using basic identity for random walk processes, a characteristic function of the ergodic distribution is written with the help of characteristics of the boundary functional SN1 (x). Moreover, a weak convergence theorem for the ergodic distribution of the standardized process Yλ(t) ≡ X(t)/λ is proved, as λ → ∞ and the limit form of the ergodic distribution is found.