THEORY OF PROBABILITY

This point includes studies on basic subjects such as:

1. Foundations of probability: existence theorems, finitely additive probabilities, 0-1 laws, integral representation of functionals, and conditional probability (according to the coherence principle and/or to the standard theory). (E. Regazzini, P. Rigo)
2. Functional and classical limit theorems: central limit problem in the study of the convergence to equilibrium of solutions of kinetic equations, convergence of empirical processes associated with sequences of non necessarily independent random elements, convergence of stochastic algorithms with a view to statistical applications. (F. Bassetti, E. Regazzini, P. Rigo)
3. Markov semigroups (in particular on non commutative algebras): contractive properties, convergence towards the invariant state, spectral gap, hypercontractivity and logarithmic Sobolev inequalities. (R. Carbone)
4. Stochastic differential equations in the Ito sense: existence and uniqueness of solutions and of invariant measures, applications to fluid dynamics.  (R. Carbone, B. Ferrario)

STATISTICS

The research activity mainly focuses on the development of methods for Bayesian inference. The main topics of interest are:

1. Bayesian nonparametric methods: construction of nonparametric priors, posterior and predictive inferences and their asymptotic properties.(F. Bassetti, A. Lijoi, E. Regazzini, P. Rigo)
2. Computational techniques: Markov Chain Monte Carlo algorithms for Bayesian nonparametric inference. (F. Bassetti, A. Lijoi)
3. Applications to industrial statistics: analysis of systems reliability. (F. Barbaini, A. Lijoi, F. Ruggeri)