期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2006
卷号：68
期号：01
出版社：Indian Statistical Institute
摘要：Some finitely additive limit theorems, which do not need a strategic setting, are proved. Let $(X_n)$ be a sequence of random variables, $\mu_n=\frac{1}{n}\sum_{i=1}^n\delta_{X_i}$ and $a_n(\cdot)=P(X_{n+1}\in\cdot\mid X_1,\dots,X_n)$, where all probability measures (both conditional and unconditional) are assessed according to de Finetti's coherence principle. In the main result, connected with Bayesian predictive inference, conditions for $\sup_{A\in\mathcal{D}}\abs{\mu_n(A)-a_n(A)}\rightarrow 0$ in probability are given, where $\mathcal{D}$ is any class of events. Under mild assumptions, it is also shown that $\sup_{A\in\mathcal{D}}\abs{\mu_n(A)-\mu_m(A)}\rightarrow 0$, in probability, whenever $(X_n)$ has stationary finite dimensional distributions. Further, asymptotic exchangeability of a certain class of sequences is proved, and this allows to extend a characterization of exchangeability due to Kallenberg (1988).
