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

Year 2012, Volume: 2 Issue: 2, 228 - 237, 01.12.2012

Tahir Khaniyev Ali Akbar Fattahpour Marandi Ihsan Unver

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 first four ergodic moments of the process X t are obtained

Keywords

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

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