Invariance Principles for Random Processes Generated by Extrema and Partial Sums of Random Variables

Assume that F is a distribution function such that for some non-degenerate distribution function G, and sequences of constants a(,n) (a(,n) positive) and b(,n), we have that, as n increases, F('n)(a(,n)x + b(,n)) converges to G(x) for every real value x. Under these conditions we prove a strong invariance principle for extremal processes analogous to the well-known invariance principle of Strassen for partial sums. In our case, the strong invariance principle yields several weak convergence results for extremal processes. This differs from the case of partial sums in that Strassen's result does not yield the central limit theorem. By a similar procedure, we also obtain a strong invariance principle for point processes in the plane.

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

• Dabrowski, Andre Robert

• Mathematics

Identifier

(UMI)AAI8302844

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71206