Speaker: Alessandro De Gregorio, Department of Statistical Sciences, Sapienza University of Rome, Italy

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

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

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Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Fractional derivatives, Inverse subordinators, Telegraph-type equations

Abstract:  In this talk, we discuss abstract integro-differential hyperbolic equations, focusing on the probabilistic representation of their solutions. Our analysis is based on fractional derivatives and non-local operators, which are powerful tools for modeling anomalous behavior and non-Markovian dynamics observed in various phenomena. We first analyze a time-fractional version of the abstract telegraph equation (involving the Caputo derivative), restricting our analysis to positive self-adjoint operators to leverage spectral theory, which includes key operators in applications, such as the fractional Laplace operator. We provide a stochastic solution to the telegraph-diffusion equation for a specific range of the fractional parameter α ∈ (0, 1/2) (see [1]). In the second part of the talk, we consider the framework arising in the case α ∈ (1/2, 1) and discuss the probabilistic representation of the solution to the telegraph equation, which generalizes the classical Kac solution (see [2]). In all cases, a crucial role is played by a time change involving the inverse of a subordinator

Biography: Alessandro De Gregorio is an Associate Professor of Probability and Mathematical Statistics at the Department of Statistical Sciences, Sapienza University of Rome. He completed his PhD in Statistical Sciences at the University of Padua between 2004 and 2006 under the supervision of Prof. Enzo Orsingher, defending a thesis titled 'Random flights: a probabilistic and statistical analysis'. His primary research interests span stochastic processes (including transport processes, time-changed stochastic processes, and fractional operators) as well as mathematical statistics, particularly statistical inference for stochastic differential equations.

Bibliography

[1] Alessandro De Gregorio, Roberto Garra. “Stochastic Solutions to Abstract Telegraph Type Equations Involving Fractional Dynamics”. In: Journal of Theoretical Probability 39:81 (2026).
[2] Alessandro De Gregorio, Francesco Iafrate. “Time-changed Random Evolutions and Fractional Telegraph Equations in Banach Spaces”. In: In preparation (2026)