GAUSSIAN SEMI-MARKOVIAN RANDOM WALK WITH A SMALL DRIFT AND WITH DELAY ON LEVEL ZERO

Abstract

In this paper the Gaussian semi-Markovian random walk process with discrete interferance of
chance, assuming that the discrete interferance of chance described by sequence of independent
random variables with gamma distribution with parameters   , ,     1, 0 are investigated.
Asymptotic formulas with the approximate coefficients of the first four moments of the process are
obtained.
Keywords: Gaussian random walk, ergodic distribution, asymptotic expansion, ladder variables