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On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications

✍ Scribed by B Bercu


Book ID
108265738
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
299 KB
Volume
111
Category
Article
ISSN
0304-4149

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On the convergence of generalized moment
✍ Ildar Ibragimov; Mikhail Lifshits πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 338 KB

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