SEMINARIO di PROBABILITÀ e STATISTICA MATEMATICA Il giorno mercoledì 28 giugno 2023, alle ore 11:00, nella Sala Professori al I Livello del Dipartimento di Matematica e Applicazioni "Renato Caccioppoli" dell'Università degli Studi di Napoli Federico II di Napoli il Prof. ALESSANDRO DE GREGORIO del Dipartimento di Scienze Statistiche dell'Università Sapienza di Roma terrà il seguente seminario: "Path dynamics of time-changed Lévy processes: a martingale approach" Abstract: Lévy processes time changed by inverse subordinators have been intensively studied in the last years. Their importance in connection with non-local operators and semi-Markov dynamics is well-understood, but, in our view, several questions remain open concerning the probabilistic structure of such processes. The time-changed Lévy processes are particularly useful to describe complex systems. The purpose of our work is to analyze the features of the sample paths of such processes, focusing on a martingale approach. We introduce the fractional Poisson random measure as the main tool dealing with the jump component of time-changed processes. A central role in the analysis is then played by the martingale properties of suitable fractional Poisson integrals associated with the jumps of the process. This allows to obtain a semi-martingale representation of time-changed processes analogous to the celebrated Lévy-Ito decomposition. The talk is based on a joint work with Francesco Iafrate (Sapienza University of Rome). Link a Teams: https://teams.microsoft.com/l/meetup-join/19%3aMQ4RZDBo_0G-K_PHxKtktVYAczOGb... Cordiali saluti, Luigia Caputo e Enrica Pirozzi -- Luigia Caputo, PhD Ricercatore Universitario di Probabilità e Statistica Matematica, Dipartimento di Matematica e Applicazioni, Università di Napoli FEDERICO II Via Cintia, 80126, NAPOLI https://www.docenti.unina.it/luigia.caputo