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 and other sciences. The main topics are stochastic evolutions, in particular stochastic differential equations in finite and infinite dimensions and particle systems, and the analysis of variational problems in probability, with applications to mathematical finance. The detailed activity of the group can be found here.

Stochastic evolutions

Existence and regularity of densities for solutions of stochastic differential equations and stochastic PDEs. SDEs with coefficients of low regularity, PDEs with problems of uniqueness and blow-up, and corresponding regularization properties due to the presence of noise. Asymptotical statistical properties for equations from fluid dynamics driven by noise. Interacting particle systems from models in neuronal and cellular biology and in physics.

People
Marta Leocata
Marco Romito [arXiv] [scholar] [mathscinet]
Research grants
PRIN 2015: Deterministic and stochastic evolution equations
Collaborators
Dirk Blömker (Augsburg)
Arnaud Debussche (ENS Bretagne)
Franco Flandoli (SNS)
Carina Geldhauser (Chebychev Lab)

Variational problems in probability, statistics and mathematical finance

Analysis on Gaussian spaces (Malliavin calculus) with applications to ordinary differential equations and PDEs. Inequalities for random variables and densities, entropic inequalities, indetermination principles, Cramér-Rao limits.  Convergence of random variational problems, laws of large numbers for empirical measures systems of interacting particle systems. Application of classic and martingale optimal transport in probability and mathematical finance.
People
Dario Trevisan
Collaborators
Giacomo De Palma (QMATH)
Martin Huesmann (Uni Bonn)
 

Past members
Franco Flandoli (SNS)
Maurizio Pratelli
Rita Giuliano