Patrizia Berti

Limit theorems for a class of identically distributed random variables

A new type of stochastic dependence for a sequence of random variables is introduced and studied. Precisely, (Xn)n≥1 is said to be conditionally identically distributed (c.i.d.), with respect to a filtration

Almost sure weak convergence of random probability measures

(\mathcal{G}_{n})_{n\geq 0}

A Glivenko-Cantelli theorem for exchangeable random variables

, if it is adapted to

Integral representation of linear functionals on spaces of unbounded functions

(\mathcal{G}_{n})_{n\geq 0}

A central limit theorem and its applications to multicolor randomly reinforced urns

and, for each n≥0, (Xk)k>n is identically distributed given the past

0-1 laws for regular conditional distributions.

\mathcal{G}_{n}

Sufficient Conditions for the Existence of Disintegrations

. In case

Rate of convergence of predictive distributions for dependent data

\mathcal{G}_{0}=\{\varnothing,\Omega\}

On Coherent Conditional Probabilities and Disintegrations

and

Strong previsions of random elements

\mathcal{G}_{n}=\sigma(X_{1},\ldots,X_{n})