NOTE: All seminars are held in person at the Department of Mathematics in Via Carlo Alberto 10, Turin.
First semester 2025/2026
Wed 29 October, 2025. Sala S, Palazzo Campana, 12:00-13:00
Mladen Savov (Sofia University)
Title: The inverse first-passage time problem for stochastic processes including Lévy processes and diffusions
Abstract: In this talk we consider the inverse first-passage time problem which consists in determining whether for a given positive random variable and a stochastic process X there is a deterministic curve such that the passage of X above it has the law of the given positive random variable. We discuss the existence and the uniqueness of those curves for arbitrary positive random variables. We exemplify our results for Lévy processes and diffusions.
This is joint work with Alexander Klump.
Wed 19 November, 2025. Sala Orsi, Palazzo Campana, 12:00-13:00
Ivana Valentić (University of Zagreb)
Title: Excursion theory for the Wright--Fisher diffusion
Abstract: The Wright--Fisher diffusion is one of the most prominent forwards-in-time models used within mathematical population genetics to describe the way in which population-level allele frequencies change over time. It falls outside the usual scope of general diffusion theory in several ways: its diffusion coefficient vanishes and fails to be Lipschitz-continuous at the boundary of its domain. In this talk I will present an excursion-based construction of the neutral Wright--Fisher diffusion. Diffusions with a single boundary point are natural subjects for excursion theory because all excursions begin and end at a single point, facilitating a Markovian construction of a path from concatenated excursions. Excursions of processes from more general sets have also been described, but the results are rarely tractable because it is in general not clear how to concatenate the resulting excursions into a path. Our construction is intermediate between these two regimes, featuring excursions which always start from a specified point, and end at one of two boundary points which determine the next starting point. (Based on work with: P. A. Jenkins, J. Koskela, V.M. Rivero, J. Sant and D. Spanò)
Wed 28 January, 2026.
Michał Gutowski (Bulgarian Academy of Sciences and Sofia University)
Title: Trapping effect of stable processes
Abstract: We are interested in the motion of a particle in a disordered medium, where the local structure of the environment induces random trapping events whose intensity depends on the particle’s position. We model this phenomenon by a $\beta$-stable process subordinated by the inverse of a $\alpha(x)$-stable subordinator, where $\beta\in(1,2]$. The resulting process is semi-Markovian. We will see that under appropriate technical assumptions on the function $\alpha(x)$, the process spends only a negligible amount of time outside a neighbourhood of the set of $\mathrm{arg\,min\,\alpha(x)}$.
The work is a natural continuation of the results provided by M. Savov and B. Toaldo in Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation, Ann. Inst. Henri Poincaré Probab. Stat., 56(4): 2640 – 2671, 2020.
Organized by
Bruno Toaldo: bruno.toaldo@unito.it
Elena Issoglio: elena.issoglio@unito.it
Sponsors
Department of Mathematics "Giuseppe Peano", University of Torino