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
Collaborators
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
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
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
People
Faculty
| Name | Surname | Personal Card | |
|---|---|---|---|
| Andrea | Agazzi | andrea.agazzi@unipi.it | |
| Mario | Maurelli | mario.maurelli@unipi.it | |
| Marco | Romito | marco.romito@unipi.it | |
| Dario | Trevisan | dario.trevisan@unipi.it |
Affiliate Members
| Name | Surname | Personal Card | |
|---|---|---|---|
| Rita | Giuliano | giuliano@dm.unipi.it | |
| Giorgio | Letta | giorgio.letta@unipi.it | |
| Maurizio | Pratelli | maurizio.pratelli@unipi.it |
Postdoctoral Fellows
| Name | Surname | Personal Card | |
|---|---|---|---|
| Alberto | Cilli | albertocilli@hotmail.it |
Ph.D. Students at the University of Pisa
| Name | Surname | Personal Card | |
|---|---|---|---|
| Leonardo | Roveri | leonardo.roveri@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) |
|---|---|---|---|---|
| 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
-
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
Past
there is no data
Visitors
Prospective
| First Name | Last Name | Affiliation |
|---|---|---|
| Milto | Hadjikyriakou | University of Central Lancashire Cyprus |
| Jonathan | Mattingly | Duke University |
Current
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 |