On a numerical approximation method of evaluating the interval transition probabilities of semi-Markov models

For the classical semi-Markov model, either time homogeneous or non-homogeneous, an examination of the convergence of the interval transition probabilities P_ij(s,t) as t → ∞ is presented using an approximation method provided by [R. De Dominics and R. Manca 1984]. Especially, we examine the dependence of the accuracy of the respective numerical method on the various values of the step h, in finding the transition interval probabilities, and we investigate the complexity of this algorithm.