THE LAPLACE TRANSFORM OF A BOUNDARY FUNCTIONAL OF THE SEMI-MARKOVIAN RANDOM WALK PROCESS WITH TWO DELAYING BARRIERS

Yıl 2016, Cilt: 6 Sayı: 1, 0 - 0, 18.07.2016

Selahattin Maden , Bahar Shamılova Gulizar Mırzoyeva

Öz

In this study, a step process of semi-Markovian random walk with delaying barriers at  and levels () and first falling moment of the process into the delaying barrier at -level, , are mathematically constructed, in this case when the random walk happens according to the Laplace’s distribution. It is given a simple form of the Laplace transformation of the distribution of the random variable.  Also the simple formulas for expectation and variance of  are obtained by the means of this Laplace transformation.