Resumen de Exchangeable sequences driven by an absolutely continuous random measure
Patrizia Berti, Luca Pratelli, Pietro Rigo
Let S be a Polish space and (Xn:n≥1) an exchangeable sequence of S-valued random variables. Let αn(⋅)=P(Xn+1∈⋅∣X1,…,Xn) be the predictive measure and α a random probability measure on S such that αn⟶weakα a.s. Two (related) problems are addressed. One is to give conditions for α≪λ a.s., where λ is a (nonrandom) σ-finite Borel measure on S. Such conditions should concern the finite dimensional distributions L(X1,…,Xn), n≥1, only. The other problem is to investigate whether ∥αn−α∥⟶a.s.0, where ∥⋅∥ is total variation norm. Various results are obtained. Some of them do not require exchangeability, but hold under the weaker assumption that (Xn) is conditionally identically distributed, in the sense of [Ann. Probab. 32 (2004) 2029–2052].
