Semi-Markov processes, time-changes and non-local equations


Friday, 2 August, 2024 - 15:00 to 16:00

Speaker : Bruno Toaldo, Dept. of Mathematics – University of Turin

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom : A link will appear here, an hour before the talk.

Organizers : Pavan Pranjivan Mehta* ( and Arran Fernandez** (

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: semi-Markov processes, non-local equations, continuous time random walk limits

Abstract: I speak about the theory of semi-Markov processes in connection with non-local equations. Therefore, I first introduce semi-Markov processes speaking about definitions in the sense of Gihman and Skorohod [1] and in the sense of Lévy (and Harlamov [2]) and then, I will explain the time-change technique in connection with semi-Markov property, and also CTRW limit processes [3]. Using suitable time-changes of Markov processes it is possible to establish a connection with several non-local equations, in time and space, with expectation of semi-Markov processes. I will speak about the classical time-change with independent inverse subordinators and also about more recent and new directions, e.g., time-change with additive components [4] and with undershooting of subordinators [5].

Biography: Bruno Toaldo is an Associate Professor of Probability at the Department of Mathematics "Giuseppe Peano”, University of Turin. Born on 1985. He earned his Ph.D from Sapienza - University of Rome in 2013. Toaldo's academic journey includes a tenure-track (Univ of Turin) and junior (Univ of Naples) researcher positions, along with a postdoctoral fellowship (Sapienza – Univ of Rome), primarily focusing on probability theory, nonlocal operators, and semi-Markov processes. He has served in numerous scientific and editorial roles. His research interests extend to modeling aspects related to anomalous transport, diffusion, and applications in mathematical finance and neuronal modeling.


[1] I. I. Gihman and A. V. Skorohod, The theory of stochastic processes II, Springer-Verlag, 1975.

[2] B. Harlamov. Continuous semi-Markov processes. John Wiley & Sons, 2013.

[3] M. M. Meerschaert and P. Straka. Semi-Markov approach to continuous time random walk limit processes. The Annals of Probability, 42(4):1699–1723, 2014.

[4] M. Savov & B. Toaldo. Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation. Annales de l'Institut Henri Poincaré (B) Probabilités and Statistiques, 56(4): 2640 - 2671, 2020.

[5] G. Ascione, E. Scalas, B. Toaldo and L. Torricelli. Work in progress, 2024.