Probability and Mathematical Statistics

The scientific activity in this area has several fruitful connections with analysis and statistics, and various applications in economics, finance, physics, biology, computer science, and other sciences. The detailed activity of the group can be found here.

Research Topics

Stochastic evolutions

The research activity is concentrated on problems of existence, regularity, statistical asymptotic behaviour, and the analysis of relevant properties of solutions of ordinary and partial differential equations with random components, with emphasis on equations from fluid dynamics. The interest spans also ordinary differential equations with non-regular coefficients, partial differential equations without uniqueness or with blow-up, and corresponding regularization properties due to noise. Problems of interacting particle systems arising from models of cortices are also considered, as well as dynamical and asymptotic properties of piecewise deterministic Markov processes.

Members
Andrea Agazzi
andrea.agazzi@unipi.it
Francesco Grotto
francesco.grotto@unipi.it
Mario Maurelli
mario.maurelli@unipi.it
Marco Romito
marco.romito@unipi.it
Collaborators
Franco Flandoli
franco.flandoli@gmail.com
Carina Geldhauser
Jonathan Mattingly
Umberto Pappalettera
Probabilistic methods in statistical learning

In recent years deep learning, through neural networks, has had an enormous impact on the development of artificial intelligence and on its possible applications. This remarkable success though has not been fully matched by theoretical results that could provide justifications of its efficacy or hints for improvements, or identify possible limitations, as well as construct methods to interpret its results. The research activity of the group in this direction is devoted to the analysis of the interaction between artificial neural networks and the theory of Gaussian processes, to the optimality and convergence of learning dynamics for neural networks, in different asymptotic regimes, to the analysis of stochastic gradient descent algorithms, to Bayes statistics for dynamical systems and reinforcement learning.

Members
Andrea Agazzi
andrea.agazzi@unipi.it
Marco Romito
marco.romito@unipi.it
Dario Trevisan
dario.trevisan@unipi.it
Jianfeng Lu
Sayan Mukherjee
Maurizio Parton
Variational problems in commutative and non-commutative probability

The main interests of this subject are analysis in Gaussian spaces, in particular Malliavin calculus, inequalities for random variables and their densities, entropic inequalities, and indeterminacy principles, in both commutative and non-commutative (quantum) settings. Other topics of interest are random optimal transportation problems, laws of large numbers for empirical measures of interacting particles, and combinatorial optimization problems in Euclidean random models.

Members
Dario Trevisan
dario.trevisan@unipi.it
Collaborators
Gian Maria Dall’Ara
Giacomo De Palma
Michael Goldman
Martin Huesmann
Stochastic processes for chemical reactions networks

The analysis is devoted to problems of large deviations for jump processes, and to structural stability conditions for their stability. The main themes in this analysis are averaging methods, duality for Markov processes, and variational inequalities. The focus is given to reaction-diffusion processes, propagation of chaos for systems of interacting particles, and to variational structures in discrete spaces, with emphasis on the out-of-equilibrium regime.

Members
Andrea Agazzi
andrea.agazzi@unipi.it
Collaborators
David Anderson
Daniele Cappelletti
Jonathan Mattingly

People

Faculty
Name Surname Email Personal Card
Andrea Agazzi
Mario Maurelli
Marco Romito
Dario Trevisan
Affiliate Members
Name Surname Email Personal Card
Rita Giuliano
Giorgio Letta
Maurizio Pratelli
Postdoctoral Fellows
Name Surname Email Personal Card
Alberto Cilli
Ph.D. Students at the University of Pisa
Name Surname Email Personal Card
Leonardo Roveri

there is no data

Ph.D. Theses supervised by members of the group

awarded by the University of Pisa
Year Name Surname Title of the Thesis Supervisor(s)
2008 Annalisa Castellucci $\phi$-Subgaussian random processes: properties and their applications Rita Giuliano
1999 Giovanni Becchere Valuation and hedging of American options in incomplete markets: minimum risk strategies Maurizio Pratelli

there is no data

Grants

• APRISE - Analysis and Probability in Science (Progetti di Ricerca di Ateneo (PRA) 2022-2023)

Principal Investigator: Marco Romito

Project period: Oct 10, 2022 – Dec 31, 2024

there is no data

Visitors

Prospective
First Name Last Name Affiliation
Milto Hadjikyriakou University of Central Lancashire Cyprus
Jonathan Mattingly Duke University

there is no data

Grouped by year
2023
First Name Last Name Affiliation From To
Michele Coghi Università di Trento Feb 06, 2023 Feb 10, 2023
Milto Hadjikyriakou University of Central Lancashire Cyprus May 15, 2023 May 19, 2023
Jonathan Mattingly Duke University Jun 12, 2023 Jul 15, 2023
Lihan Wang Istituto Max Planck Lipsia Feb 11, 2023 Feb 15, 2023
2022
First Name Last Name Affiliation From To
Angelo Lucia Universidad Complutense de Madrid Dec 01, 2022 Dec 02, 2022