# An Anscombe-type theorem

Berti, Patrizia and Crimaldi, Irene and Pratelli, Luca and Rigo, Pietro An Anscombe-type theorem. Journal of Mathematical Sciences, 196 (1). pp. 15-22. ISSN 1072-3374 (2014)

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## Abstract

Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well.

Item Type: Article 10.1007/s10958-013-1629-6 Proceedings of the XXV International Seminar on Stability Problems for Stochastic Models, Maiori (Salerno), Italy, September 20–24, 2005. Anscombe theorem, Exchangeability, Random indices, Random sums, Stable convergence Q Science > QA Mathematics Economics and Institutional Change Irene Crimaldi 21 Jun 2013 11:23 29 Jan 2014 14:34 http://eprints.imtlucca.it/id/eprint/1622

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