Some Almost Sure Convergence Results

The first chapter of the thesis consists of an almost sure invariance principle for random variables in the Domain of Attraction of a Stable Law. Let {Y,Y(,1),Y(,2),...} be a sequence of i.i.d. symmetric random variables with Y in the domain of attraction of X where X is symmetric and stable of index (alpha). Suppose {a(,n)}, 0 ) 0 as i (--->) (INFIN). This extends an analogous result of Stout's where the more restrictive assumption is made that Y is in the domain of normal attraction of X.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Fisher, Evan David

• Mathematics

Language dc:language

eng

Identifier

(UMI)AAI8203458

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/68186