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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 |
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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