Three-term asymptotic expansion: A semi-Markovian random walk with a generalized beta distributed interference of chance |
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| Authors: | Tülay Kesemen Tahir Khaniyev Çisem Öçal |
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| Institution: | 1. Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon, Turkey;2. Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey;3. Azerbaijan National Academy of Sciences, Institute of Control Systems, Baku, Azerbaijan |
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| Abstract: | A semi-Markovian random walk process (X(t)) with a generalized beta distribution of chance is considered. The asymptotic expansions for the first four moments of the ergodic distribution of the process are obtained as E(ζn) → ∞ when the random variable ζn has a generalized beta distribution with parameters (s, S, α, β); ?α, β > 1,?0? ? s < S < ∞. Finally, the accuracy of the asymptotic expansions is examined by using the Monte Carlo simulation method. |
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| Keywords: | Asymptotic expansions generalized beta distribution semi-Markovian random walk process discrete interference of chance |
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