{"id":60,"date":"2022-03-16T22:31:48","date_gmt":"2022-03-16T22:31:48","guid":{"rendered":"https:\/\/www.dm.unipi.it\/research\/probability-and-mathematical-statistics\/"},"modified":"2026-01-23T10:11:13","modified_gmt":"2026-01-23T09:11:13","slug":"probability-and-mathematical-statistics","status":"publish","type":"page","link":"https:\/\/www.dm.unipi.it\/research\/areas\/probability-and-mathematical-statistics\/","title":{"rendered":"Probability and Mathematical Statistics"},"content":{"rendered":"\n

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<\/a>.<\/p>\n\n\n\n

The group runs a Seminar Series: more info can be found at this link<\/a>.<\/p>\n\n\n\n

<\/div>\n\n\n\n

Research Topics<\/h4>\n\n\n\n
Stochastic evolutions<\/h5>
\n

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, corresponding regularization properties due to noise, and simplified models of turbulence. Problems of interacting particle systems arising from models of vortices are also considered, as well as dynamical and asymptotic properties of piecewise deterministic Markov processes.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nFrancesco Grotto\n\n<\/span>
\n<\/i>francesco.grotto@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nMario Maurelli\n\n<\/span>
\n<\/i>mario.maurelli@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nFrancesco Morandin\n\n<\/span>
\n<\/i>francesco.morandin@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nAikaterini Papagiannouli\n\n<\/span>
\n<\/i>aikaterini.papagiannouli@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nMarco Romito\n\n<\/span>
\n<\/i>marco.romito@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nZdzislaw Brzezniak (York University)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMichele Coghi (Universit\u00e0 degli Studi di Trento)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nFranco Flandoli (SNS, Pisa)\n\n<\/span>
\n<\/i>franco.flandoli@gmail.com<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nLucio Galeati (Universit\u00e0 degli Studi dell'Aquila)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nCarina Geldhauser (ETH Z\u00fcrich)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nSotirios Kotitsas (\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL))\n\n<\/span>
\n<\/i>sotirios.kotitsas@epfl.ch<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nJonathan Mattingly (Duke University)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nUmberto Pappalettera (Universit\u00e4t Basel)\n\n<\/span>
\n<\/i>umberto.pappallera@unibas.ch<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Probabilistic methods in statistical learning<\/h5>
\n

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.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nFrancesco Morandin\n\n<\/span>
\n<\/i>francesco.morandin@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nAikaterini Papagiannouli\n\n<\/span>
\n<\/i>aikaterini.papagiannouli@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nMarco Romito\n\n<\/span>
\n<\/i>marco.romito@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nDario Trevisan\n\n<\/span>
\n<\/i>dario.trevisan@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nAndrea Agazzi (Universit\u00e4t Bern)\n\n<\/span>
\n<\/i>andrea.agazzi@unibe.ch<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nJianfeng Lu (Duke University)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nSayan Mukherjee (Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMaurizio Parton (Universit\u00e0 degli Studi \u201cGabriele D\u2019Annunzio\u201d Chieti - Pescara)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Variational problems in commutative and non-commutative probability<\/h5>
\n

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.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nDario Trevisan\n\n<\/span>
\n<\/i>dario.trevisan@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nGian Maria Dall\u2019Ara (SNS, Pisa, INdAM)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nGiacomo De Palma (Universit\u00e0 di Bologna)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMichael Goldman (CNRS, \u00c9cole Polytechnique)\n\n<\/span>
\n<\/i>michael.goldman@cnrs.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMartin Huesmann (Universit\u00e4t M\u00fcnster)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Stochastic processes for chemical reactions networks<\/h5>
\n

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.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nMario Maurelli\n\n<\/span>
\n<\/i>mario.maurelli@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nSilvia Morlacchi\n\n<\/span>
\n<\/i>silvia.morlacchi@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nDavid Anderson (University of Wisconsin-Madison)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nDaniele Cappelletti (Politecnico di Torino)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nJonathan Mattingly (Duke University)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n\n

People<\/h4>\n\n\n\n
Faculty<\/h5>
\n\n\n\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nEmail<\/th>\nPersonal Card<\/th>\n<\/tr><\/thead>
Mario<\/td>\nMaurelli<\/td>\n<\/i>mario.maurelli@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Francesco<\/td>\nMorandin<\/td>\n<\/i>francesco.morandin@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Aikaterini<\/td>\nPapagiannouli<\/td>\n<\/i>aikaterini.papagiannouli@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Marco<\/td>\nRomito<\/td>\n<\/i>marco.romito@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Dario<\/td>\nTrevisan<\/td>\n<\/i>dario.trevisan@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Affiliate Members<\/h5>
\n\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nEmail<\/th>\nPersonal Card<\/th>\n<\/tr><\/thead>
Rita<\/td>\nGiuliano<\/td>\n<\/i>rita.giuliano@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Giorgio<\/td>\nLetta<\/td>\n<\/i>giorgio.letta@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Maurizio<\/td>\nPratelli<\/td>\n<\/i>maurizio.pratelli@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Former Members<\/h5>
\n\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\n<\/tr><\/thead>
Andrea<\/td>\nAgazzi<\/td>\n<\/tr>\n
Giacomo Filippo<\/td>\nDi Ges\u00f9<\/td>\n<\/tr>\n
Franco<\/td>\nFlandoli<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Postdoctoral Fellows<\/h5>
\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nEmail<\/th>\nPersonal Card<\/th>\n<\/tr><\/thead>
Silvia<\/td>\nMorlacchi<\/td>\n<\/i>silvia.morlacchi@dm.unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Ph.D. Students at the University of Pisa<\/h5>
\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nEmail<\/th>\nPersonal Card<\/th>\n<\/tr><\/thead>
Eloy<\/td>\nMosig<\/td>\n<\/i>eloy.mosig@phd.unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Samuele<\/td>\nSaviozzi<\/td>\n<\/i>samuele.saviozzi@phd.unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Ph.D. Students at other institutions<\/h5>
\n\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nAffiliation<\/th>\n<\/tr><\/thead>
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Shuaijie<\/td>\nJiao<\/td>\nAcademy of Mathematics and System Sciences of the Chinese Academy of Sciences<\/td>\n<\/tr>\n
Francesco<\/td>\nTriggiano<\/td>\nSNS, Pisa<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n\n

Ph.D. Theses supervised by members of the group<\/h4>\n\n\n\n
awarded by the University of Pisa<\/h5>
\n\n\n\n\n\n\n\n\n
Year<\/th>\nName<\/th>\nSurname<\/th>\nTitle of the Thesis<\/th>\n Supervisor(s)<\/th>\n<\/tr><\/thead>
2025<\/td>\nLeonardo<\/td>\nRoveri<\/td>\nStochastic Fluids - Theoretical Models and Machine Learning Applications<\/td>\nMarco Romito<\/a><\/td>\n<\/tr>\n
2017<\/td>\nValeria<\/td>\nDe Mattei<\/td>\nNew approaches to Mean Field Game Theory<\/td>\nFranco Flandoli<\/td>\n<\/tr>\n
2008<\/td>\nAnnalisa<\/td>\nCastellucci<\/td>\n$\\phi$-Subgaussian random processes: properties and their applications<\/td>\nRita Giuliano<\/a><\/td>\n<\/tr>\n
1999<\/td>\nGiovanni<\/td>\nBecchere<\/td>\nValuation and hedging of American options in incomplete markets: minimum risk strategies<\/td>\nMaurizio Pratelli<\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
awarded by another institution<\/h5>
\n\n\n\n\n\n
Year<\/th>\nName<\/th>\nSurname<\/th>\nTitle of the Thesis<\/th>\n Institution<\/th>\n Supervisor(s)<\/th>\n<\/tr><\/thead>
2025<\/td>\nMarco<\/td>\nBagnara<\/td>\nAnomalous Regularization and Blow-up Prevention in Stochastic Fluid Dynamics Models<\/td>\nSNS, Pisa<\/td>\nFranco Flandoli and Mario Maurelli<\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n\n

Grants<\/h4>\n\n\n\n
Current<\/h5>
\n\n