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.

An Anscombe-type theorem

RIGO, PIETRO
2014

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/741619
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