LIMIT DISTRIBUTION FOR SEMI-MARKOVIAN RANDOM WALK WITH A GENERALIZED DELAYING BARRIER

In this study, a semi – Markovian random walk process (X)t)) with a generalized delaying barrier is considered and ergodic theorem for this process is proved under some weak conditions. Moreover, the characteristic function of the ergodic distribution of the process x(t)is expressed by characteristic function of a boundary functional SN(z). Then, using this representation, it is shown that the ergodic distribution of the standardized process YX(t)=X(T)/Xconverges to a limit distribution, when . Finally, the explicit form of the limit distribution is obtained.

Keywords:

Semi - Markovian random walk , Delaying barrier , Ergodic distribution , Asymptotic expansion , Weak convergence , Limit distribution