ASYMPTOTIC EXPANSIONS FOR THE ERGODIC MOMENTS OF A SEMI-MARKOVIAN RANDOM WALK WITH A GENERALIZED DELAYING BARRIER

ASYMPTOTIC EXPANSIONS FOR THE ERGODIC MOMENTS OF A SEMI-MARKOVIAN RANDOM WALK WITH A GENERALIZED DELAYING BARRIER

Tahir Khaniyev    Ali Akbar Fattahpour Marandi    Ihsan Unver    

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Abstract

In this study, a semi-Markovian random walk process (X(t)) with a generalized delaying barrier is considered and the ergodic theorem for this process is proved under some weak conditions. Then, the exact expressions and asymptotic expansions for the rst four ergodic moments of the process X(t) are obtained.

Keywords

Semi - Markovian random walk, delaying barrier, ergodic distribution, ergodic moments, asymptotic expansion, ladder height.