Abstract. Given a four-dimensional sequence of independent identically located and positive random variables, a process with differentiable semi-Markov walk delayed by a screen at zero is considered. An explicit form of the Laplace transform in time, the Laplace–Stieltjes transform of the ergodic distribution of a process with differentiable semi-Markov walk with delaying screen at zero is found.

Keywords: semi-Markov process, differential walk, delaying screen, Laplace transform, Erlang distribution.