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

Enzo Orsingher; Costantino Ricciuti; Bruno Toaldo

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arXiv · 1701.02905

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

Enzo Orsingher·Costantino Ricciuti·Bruno Toaldo

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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.

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BibTeX RIS

Enzo Orsingher, Costantino Ricciuti, Bruno Toaldo. 2017-09-18. On semi-Markov processes and their Kolmogorov's integro-differential equations. https://arxiv.org/abs/1701.02905

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