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On the convergence of generalized moments in almost sure central limit theorem

✍ Scribed by Ildar Ibragimov; Mikhail Lifshits

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
338 KB
Volume
40
Category
Article
ISSN
0167-7152

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✦ Synopsis

Let {~k} be the normalized sums corresponding to a sequence of i.i.d, variables with zero mean and unit variance. Define random measures n k=l and let G be the normal distribution. We show that for each continuous function h satisfying f h dG<~ and a mild regularity assumption, one has limfhdO,=fhdG a.s. n~

πŸ“œ SIMILAR VOLUMES

On the almost sure central limit theorem
On the almost sure central limit theorem for randomly indexed sums
✍ A. Krajka; J. Wasiura πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 169 KB πŸ‘ 1 views

## Abstract Let {__S~n~__, __n__ β‰₯ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {__S~Nn~__, __n__ β‰₯ 1}, where {__N~n~__, __n__ β‰₯ 1} is a sequence of positive integer‐valued random varia