𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Limit distributions for products of sums

✍ Scribed by Yongcheng Qi

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
126 KB
Volume
62
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

Let {X; X n ; n¿ 1} be a sequence of independent and identically distributed positive random variables and set S n = n j=1 X j for n ¿ 1. This paper proves that properly normalized products of the partial sums, ( n j=1 S j =n! n ) =An , converges in distribution to some nondegenerate distribution when X is in the domain of attraction of a stable law with index ∈ (1; 2].

πŸ“œ SIMILAR VOLUMES

Limiting behavior of weighted sums with
Limiting behavior of weighted sums with stable distributions
✍ Chen Pingyan πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 115 KB

We present an integral test to determine the limiting behavior of weighted sums of independent, symmetric random variables with stable distributions, and deduce Chover-type laws of the iterated logarithm for them.

A distributional limit law for the conti
A distributional limit law for the continued fraction digit sum
✍ Marc KessebΓΆhmer; Mehdi Slassi πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 186 KB

## Abstract We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalised fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For

Limit Theorems for Sums of Random Fuzzy
Limit Theorems for Sums of Random Fuzzy Sets
✍ Marco Dozzi; Ely Merzbach; Volker Schmidt πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 100 KB

We consider limit theorems for counting processes generated by Minkowski sums of random fuzzy sets. Using support functions, we prove almost-sure convergence for a renewal process indexed by fuzzy sets in an inner-product vector space. We also get convergence for the associated containment renewal f