Elenco seminari del ciclo ``Seminari di Probabilità''

16 Mag 2018
Existence of proper regular conditional distributions
Pietro Rigo
In the first part of the talk, mainly of the heuristic type, some basic notions (such as regularity, properness, disintegrability) are recalled and some examples are discussed. The second part is more technical and is devoted to some results and their implications. In the classical (Kolmogorovian) framework, a few 0-1 laws for regular conditional distributions are stated. Special attention is paid to the tail and the symmetric sigma- fields. In the coherent (de Finettian) framework, with reference to a Bayesian inferential problem, the existence of posterior distributions that make sufficient a given statistics, or make optimal a given estimator, is discussed. Finally, some compatibility problems for conditional distributions are mentioned, and a few asymptotic results are stated
16 Mag 2018
Existence of proper regular conditional distributions
Pietro Rigo (Università di Pavia)
In the first part of the talk, mainly of the heuristic type, some basic notions (such as regularity, properness, disintegrability) are recalled and some examples are discussed. The second part is more technical and is devoted to some results and their implications. In the classical (Kolmogorovian) framework, a few 0-1 laws for regular conditional distributions are stated. Special attention is paid to the tail and the symmetric sigma- fields. In the coherent (de Finettian) framework, with reference to a Bayesian inferential problem, the existence of posterior distributions that make sufficient a given statistics, or make optimal a given estimator, is discussed. Finally, some compatibility problems for conditional distributions are mentioned, and a few asymptotic results are stated
22 Nov 2017
seminario di probabilità
Probabilisti e statistici italiani del secolo scorso
Eugenio Regazzini
Il XX è stato, fra altre cose, anche il secolo della rinascita della probabilità e della statistica nelle comunità scientifiche più avanzate dell'occidente. Questo seminario si propone di illustrare il contributo degli italiani a tale processo, a partire dalle questioni che, polarizzando l'interesse di alcuni nostri studiosi di forte ingegno, portarono alla formulazione di teorie originali ed al conseguimento di pregevoli risultati destinati a durare nel tempo. Di essi si darà cenno, breve ma sperabilmente sufficiente a chiarirne valore e ruolo in relazione allo sviluppo generale delle scienze e dei metodi, insieme a qualche considerazione sulle caratteristiche umane e professionali degli Autori.
13 Set 2017
seminario di probabilità
$N$-player games and mean field games with absorption
Luciano Campi
We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It{\^o} equations with absorption on first exit from a bounded open set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean field game, the renormalization appears in form of a conditional law. We justify our definition of solution in the usual way, that is, by showing that a solution of the mean field game induces approximate Nash equilibria for the $N$-player games with approximation error tending to zero as $N$ tends to infinity. This convergence is established provided the diffusion coefficient is non-degenerate. The degenerate case is more delicate and gives rise to counter-examples. This talk is based on a joint work with Markus Fischer (Università degli Studi di Padova).