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Title: Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance
Authors: Aliyev, Rovshan
Küçük, Zafer
Khaniyev, Tahir
Keywords: Semi-Markovian random walk
A discrete interference of chance
Ergodic distribution
Ergodic moments
Asymptotic expansion
Monte Carlo simulation method
Issue Date: 2010
Publisher: Elsevier Science 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 ergodic distribution of the process X(t) are obtained when the random variable which is describing a discrete interference of chance, has a triangular distribution in the interval Is, SI with center (S + s)/2. Based on these results, the asymptotic expansions with three-term are obtained for the first four moments of the ergodic distribution of X(t), as a (S - s)/2 -> infinity. Furthermore, the asymptotic expansions for the variance, skewness and kurtosis of the ergodic distribution of the process X(t) are established. Finally, by using Monte Carlo experiments it is shown that the given approximating formulas provide high accuracy even for small values of parameter a. (c) 2010 Elsevier Inc. All rights reserved.
ISSN: 0307-904X
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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