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.
P. Berti, I. Crimaldi, L. Pratelli, P. Rigo (2014). An Anscombe-type theorem. JOURNAL OF MATHEMATICAL SCIENCES, 196, 15-22 [10.1007/s10958-013-1629-6].
An Anscombe-type theorem
P. Rigo
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.File in questo prodotto:
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