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.

The group runs a Seminar Series: more info can be found at this link.

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
Aikaterini Papagiannouli
aikaterini.papagiannouli@unipi.it
Marco Romito
marco.romito@unipi.it
Collaborators
Franco Flandoli (SNS, Pisa)
franco.flandoli@gmail.com
Carina Geldhauser (Lund University)
Jonathan Mattingly (Duke University)
Umberto Pappalettera (SNS, Pisa)
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
Aikaterini Papagiannouli
aikaterini.papagiannouli@unipi.it
Marco Romito
marco.romito@unipi.it
Dario Trevisan
dario.trevisan@unipi.it
Collaborators
Jianfeng Lu (Duke University)
Sayan Mukherjee (Max-Planck-Institut für Mathematik in den Naturwissenschaften)
Maurizio Parton (Università degli Studi “Gabriele D’Annunzio” Chieti - Pescara)
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 (SNS, Pisa, INdAM)
Giacomo De Palma (Università di Bologna)
Michael Goldman (CNRS, Université Paris Cité)
Martin Huesmann (Universität Münster)
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 (University of Wisconsin-Madison)
Daniele Cappelletti (Politecnico di Torino)
Jonathan Mattingly (Duke University)

People

Faculty
Name Surname Email Personal Card
Andrea Agazzi andrea.agazzi@unipi.it
Mario Maurelli mario.maurelli@unipi.it
Aikaterini Papagiannouli aikaterini.papagiannouli@unipi.it
Marco Romito marco.romito@unipi.it
Dario Trevisan dario.trevisan@unipi.it
Affiliate Members
Name Surname Email Personal Card
Rita Giuliano rita.giuliano@unipi.it
Giorgio Letta giorgio.letta@unipi.it
Maurizio Pratelli maurizio.pratelli@unipi.it
Former Members
Name Surname
Giacomo Filippo Di Gesù
Franco Flandoli
Postdoctoral Fellows
Name Surname Email Personal Card
Essebei Fares essebeifares@gmail.com
Ph.D. Students at the University of Pisa
Name Surname Email Personal Card
Eloy Mosig eloy.mosig@phd.unipi.it
Leonardo Roveri leonardo.roveri@phd.unipi.it
Samuele Saviozzi samuele.saviozzi@phd.unipi.it
Ph.D. Students at other institutions

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)
2017 Valeria De Mattei New approaches to Mean Field Game Theory Franco Flandoli
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
awarded by another institution

there is no data

Grants

Current
Past

there is no data

Visitors

Prospective
First Name Last Name Affiliation
Klas Modin Chalmers University of Technology, University of Gothenburg
Current

there is no data

Grouped by year
2024
First Name Last Name Affiliation From To
Juliette Achddou Università degli Studi di Milano (La Statale) Jun 03, 2024 Jun 04, 2024
Youngsoo Baek Duke University Jul 10, 2024 Jul 12, 2024
Patrick Charbonneau Duke University Mar 19, 2024 Mar 20, 2024
Massimiliano Datres Università degli Studi di Trento Apr 08, 2024 Apr 11, 2024
Giacomo Filippo Di Gesù Sapienza Università di Roma May 30, 2024 May 30, 2024
Sotiris Kotitsas Università di Pisa Jul 02, 2024 Jul 05, 2024
Claudio Macci Università degli Studi di Roma Tor Vergata Mar 25, 2024 Mar 27, 2024
Daniele Malpetti Istituto Dalle Molle di studi sull'intelligenza artificiale (IDSIA USI-SUPSI) Jun 03, 2024 Jun 04, 2024
Klas Modin Chalmers University of Technology, University of Gothenburg Sep 10, 2024 Sep 13, 2024
Luca Papariello Business Integration Partners (BIP) S.p.A. Jun 03, 2024 Jun 04, 2024
Federico Pasqualotto University of California, Berkeley May 28, 2024 May 29, 2024
Francesco Preta Centre Marc Bloch May 27, 2024 May 29, 2024
Sara Svaluto Ferro Università di Verona Jun 03, 2024 Jun 04, 2024
2023
First Name Last Name Affiliation From To
Giuseppe Cannizzaro University of Warwick Sep 17, 2023 Sep 22, 2023
Sandra Cerrai University of Maryland Jun 16, 2023 Jul 15, 2023
Michele Coghi Università degli Studi di Trento Feb 06, 2023 Feb 10, 2023
Ernesto De Vito Università di Genova Oct 16, 2023 Oct 16, 2023
Giacomo Filippo Di Gesù Sapienza Università di Roma Sep 19, 2023 Sep 19, 2023
Giuseppe Genovese Universität Zürich Jun 14, 2023 Jun 16, 2023
Milto Hadjikyriakou University of Central Lancashire Cyprus May 15, 2023 May 19, 2023
Lucie Laurence INRIA (Paris) Nov 27, 2023 Dec 01, 2023
Mauro Mariani Higher School of Economics (HSE) University Apr 28, 2023 May 28, 2023
Jonathan Mattingly Duke University Jun 11, 2023 Jul 22, 2023
Riccardo Montalto Università degli Studi di Milano (La Statale) Apr 03, 2023 Apr 07, 2023
Sayan Mukherjee Max-Planck-Institut für Mathematik in den Naturwissenschaften Jun 16, 2023 Jun 16, 2023
Aikaterini Papagiannouli Max-Planck-Institut für Mathematik in den Naturwissenschaften Jun 06, 2023 Jun 16, 2023
Chiara Saffirio Universität Basel Jun 13, 2023 Jun 16, 2023
Vittoria Silvestri Sapienza Università di Roma Apr 18, 2023 Apr 19, 2023
Lihan Wang Max-Planck-Institut für Mathematik in den Naturwissenschaften Feb 11, 2023 Feb 15, 2023
Pavlos Zoubouloglou The University of North Carolina at Chapel Hill Jun 28, 2023 Jul 02, 2023
2022
First Name Last Name Affiliation From To
Angelo Lucia Universidad Complutense de Madrid Dec 01, 2022 Dec 02, 2022
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