𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the almost sure central limit theorem and domains of attraction

✍ Scribed by István Berkes

Publisher
Springer
Year
1995
Tongue
English
Weight
673 KB
Volume
102
Category
Article
ISSN
1432-2064

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On the almost sure central limit theorem
On the almost sure central limit theorem for randomly indexed sums
✍ A. Krajka; J. Wasiura 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 169 KB 👁 1 views

## Abstract Let {__S~n~__, __n__ ≥ 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__ ≥ 1}, where {__N~n~__, __n__ ≥ 1} is a sequence of positive integer‐valued random varia

On the convergence of generalized moment
On the convergence of generalized moments in almost sure central limit theorem
✍ Ildar Ibragimov; Mikhail Lifshits 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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