Moderate deviation of intersection of ranges of random walks in the stable case

Author

Justin Anthony GrievesFollow

Date of Award

12-2011

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Xia Chen

Committee Members

Jan Rosinski, Carl Wagner, Mary Leitnaker

Abstract

Given p independent, symmetric random walks on d-dimensional integer lattice that are the domain of attraction for a stable distribution, we calculate the moderate deviation of the intersection of ranges of the random walks in the case where the walks intersect infinitely often as time goes to infinity. That is to say, we establish a weak law convergence of intersection of ranges to intersection local time of stable processes and use this convergence as a link to establish deviation results.

Recommended Citation

Grieves, Justin Anthony, "Moderate deviation of intersection of ranges of random walks in the stable case. " PhD diss., University of Tennessee, 2011.
https://trace.tennessee.edu/utk_graddiss/1184