A SEMI – MARKOVIAN RANDOM WALK WITH GENERALIZED DELAYING BARRIER

In this study, a semi-Markovian random walk process with a generalized delaying barrier and its three boundary functionals (N1 , τ1 , γ1 )are mathematically constructed. Under some weak conditions, exact expressions and asymptotic expansions for the expected values and variances of these boundary functionals are obtained.

Keywords:

Semi – Markovian random walk , Boundary functional , Asymptotic expansion , Renewal function