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STATISTICAL INFERENCE OF STOCHASTIC DIFFERENTIAL
EQUATIONS DRIVEN BY GAUSSIAN NOISE
by
Michael Moers
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
August 2012
Copyright 2012 Michael Moers
Object Description
| Title | Statistical inference of stochastic differential equations driven by Gaussian noise |
| Author | Moers, Michael |
| Author email | moers@usc.edu;mmoers@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2012-06-14 |
| Date submitted | 2012-07-25 |
| Date approved | 2012-07-25 |
| Restricted until | 2012-07-25 |
| Date published | 2012-07-25 |
| Advisor (committee chair) | Lototsky, Sergey |
| Advisor (committee member) |
Mikulevicius, Remigijus Haas, Stephan |
| Abstract | The objective of this thesis is to study statistical inference of first and second order ordinary differential equations driven by continuous Gaussian noise under continous time observations. ❧ The Gaussian process can be defined by a stochastic integral of a time-dependent triangular deterministic kernel with respect to standard Brownian motion. Especially, we do not assume the process to be Markovian nor a semimartingale. An important example for such a process is fractional Brownian motion. ❧ The thesis is focussed on (a) properties of these Gaussian processes (b) maximum likelihood estimation (c) asymptotic distribution of finite sample distribution of least squares type estimator. |
| Keyword | statistical inference; Volterra processes; maximum-likelihood estimation; fractional Brownian motion |
| 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 |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Moers, Michael |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume4/etd-MoersMicha-980.pdf |
Description
| Title | Page 1 |
| Full text | STATISTICAL INFERENCE OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY GAUSSIAN NOISE by Michael Moers A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) August 2012 Copyright 2012 Michael Moers |
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