On semi-Markov processes and their Kolmogorov's integro-differential equations

Enzo Orsingher, Costantino Ricciuti, Bruno Toaldo

Published 2017-01-11Version 1

Semi-Markov processes are a generalization of Markov processes since the exponential distribution of time intervals is replaced with an arbitrary distribution. This paper provides an integro-differential form of the Kolmogorov's backward equations for a large class of homogeneous semi-Markov processes, having the form of a Volterra integro-differential equation. An equivalent evolutionary (differential) form of the equations is also provided. Weak limits of semi-Markov processes are also considered and their corresponding integro-differential Kolmogorov's equations are identified.