On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance

Authors : Tülay KESEMEN

Pages : 299-307

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Publication Date : 2013-03-01

Article Type : Other Papers

Abstract :In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance insert ignore into journalissuearticles values(Xinsert ignore into journalissuearticles values(t);); is considered.It is assumed that therandom variables {ζn } , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters insert ignore into journalissuearticles values(α, λ);, α > 1, λ >0. Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process Xinsert ignore into journalissuearticles values(t); are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process Xinsert ignore into journalissuearticles values(t); are established.
Keywords : Semi Markovian random walk, a discrete interference of chance, Weibulldistribution, ergodic distribution, asymptotic expansion, ladder variables