On semi-Markov processes and their Kolmogorov's integro-differential equations
Probability
2017-09-20 v2
Abstract
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 an abstract Volterra integro-differential equation. An equivalent evolutionary (differential) form of the equations is also provided. Fractional equations in the time variable are a particular case of our analysis. Weak limits of semi-Markov processes are also considered and their corresponding integro-differential Kolmogorov's equations are identified.
Keywords
Cite
@article{arxiv.1701.02905,
title = {On semi-Markov processes and their Kolmogorov's integro-differential equations},
author = {Enzo Orsingher and Costantino Ricciuti and Bruno Toaldo},
journal= {arXiv preprint arXiv:1701.02905},
year = {2017}
}