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 nonregular coefficients, partial differential equations without uniqueness or with blowup, 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
Collaborators
Variational problems in commutative and noncommutative 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 noncommutative (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
Collaborators
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 reactiondiffusion processes, propagation of chaos for systems of interacting particles, and to variational structures in discrete spaces, with emphasis on the outofequilibrium regime.
Members
Collaborators
People
Faculty
Name  Surname  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  Personal Card  

Rita  Giuliano  giuliano@dm.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  Personal Card  

Alberto  Cilli  albertocilli@hotmail.it  
Essebei  Fares  essebeifares@gmail.com 
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) 

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

Convergence and Stability of Reaction and Interaction Network Dynamics (ConStRAINeD) (Prin 2022)
Principal Investigator: Daniele Cappelletti
Coordinator of the Research Unit: Andrea Agazzi
Project period: Sep 28, 2023 – Sep 27, 2025

Understanding the LEarning process of QUantum Neural networks (LeQun) (Prin 2022)
Principal Investigator: Giacomo De Palma
Coordinator of the Research Unit: Dario Trevisan
Project period: Sep 28, 2023 – Sep 27, 2025

Noise in fluid dynamics and related models (Prin 2022)
Principal Investigator: Franco Flandoli
Coordinator of the Research Unit: Marco Romito
Project period: Sep 28, 2023 – Sep 27, 2025

APRISE  Analysis and Probability in Science (Progetti di Ricerca di Ateneo (PRA) 20222023)
Principal Investigator: Marco Romito
Project period: Oct 10, 2022 – Dec 31, 2024
Past
there is no data
Visitors
Prospective
there is no data
Current
there is no data
Grouped by year
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 di Trento  Feb 06, 2023  Feb 10, 2023 
Giacomo Filippo  Di Gesù  Sapienza Università di Roma  Sep 19, 2023  Sep 19, 2023 
Giuseppe  Genovese  Institut für Mathematik  Universität Zürich  Jun 14, 2023  Jun 16, 2023 
Milto  Hadjikyriakou  University of Central Lancashire Cyprus  May 15, 2023  May 19, 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  MaxPlanckInstitut für Mathematik in den Naturwissenschaften  Jun 16, 2023  Jun 16, 2023 
Aikaterini  Papagiannouli  MaxPlanckInstitut 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  MaxPlanckInstitut für Mathematik in den Naturwissenschaften  Feb 11, 2023  Feb 15, 2023 
Pavlos  Zoubouloglu  University of North Carolina  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 