Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/6322
Title: Asymptotic Expansions for the Moments of the Semi-Markovian Random Walk with Gamma Distributed Interference of Chance
Authors: Aliyev, Rovshan
Khaniyev, Tahir
Kesemen, Tülay
Keywords: Asymptotic expansions
Boundary functional
Discrete interference of chance
Ergodic distribution
Gamma distribution
Ladder variables
Moments
Semi-Markovian random walk
Issue Date: 2010
Publisher: Taylor & Francis Inc
Abstract: In this study, a semi-Markovian random walk with a discrete interference of chance (X(t)) is considered and under some weak assumptions the ergodicity of this process is discussed. The exact formulas for the first four moments of the ergodic distribution of the process X(t) are obtained when the random variable zeta(1), which describes a discrete interference of chance, has a gamma distribution with parameters (alpha, lambda), alpha > 1, lambda > 0. Based on these results, the asymptotic expansions are obtained for the first four moments of the ergodic distribution of the process X(t), as lambda -> 0. Furthermore, the asymptotic expansions for the skewness and kurtosis of the ergodic distribution of the process X(t) are established. Finally, it is discussed that the alternative estimations for the stationary characteristics of this process can be offered by using obtained asymptotic expansions.
URI: https://doi.org/10.1080/03610920802662150
https://hdl.handle.net/20.500.11851/6322
ISSN: 0361-0926
1532-415X
Appears in Collections:Endüstri Mühendisliği Bölümü / Department of Industrial Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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