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MIXING CONDITIONS AND RETURN TIMES
ON MARKOV TOWERS
by
Yiannis Psiloyenis
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2008
Copyright 2008 Yiannis Psiloyenis
Object Description
| Title | Mixing conditions and return times on Markov Towers |
| Author | Psiloyenis, Yiannis |
| Author email | psiloyen@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-05-23 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-06-24 |
| Advisor (committee chair) | Haydn, Nicolai |
| Advisor (committee member) |
Baxendale, Peter Jonckheere, Edmond Lototsky, Sergey |
| Abstract | This dissertation discusses mixing properties derived on non-uniformly hyperbolic dynamical systems which admit a Markov-Tower structure. For systems with exponential and polynomial decay of the tails of the return map we derive alpha-mixing conditions at exponential and polynomial rates, respectively. The motivation is to use these mixing conditions, on eligible systems, to approximate the law of the hitting and return times to a set of small measure.; In the first chapter we set up the problem and derive mixing conditions. In the next chapter we give a brief discussion on Stein method and in chapter three we study the hitting and multiple-return times for α-mixing dynamical systems in general. Under the given rates of mixing we use the Stein method to show that the return time of order k to a cylinder A can be approximated by a simple distribution for which sharp error bounds, independent of the order k, are obtained as well. Additionally, we conclude that the distribution of hitting times, suitably rescaled, can be approximated by an exponential distribution with mean 1.; As an application we show that the findings for the return and hitting times can be applied, through the construction of aMarkov Tower, to the Gaspard-Wang map which is broadly used in Physics. |
| Keyword | Stein method; Poisson approximation; hyperbolic dynamical systems; Markov towers; hitting time; return times; mixing |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m1288 |
| Rights | Psiloyenis, Yiannis |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Psiloyenis-20080624 |
| Archival file | uscthesesreloadpub_Volume44/etd-Psiloyenis-20080624.pdf |
Description
| Title | Page 1 |
| Full text | MIXING CONDITIONS AND RETURN TIMES ON MARKOV TOWERS by Yiannis Psiloyenis A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2008 Copyright 2008 Yiannis Psiloyenis |
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