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ON SPECTRAL APPROXIMATIONS OF
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
DRIVEN BY POISSON NOISE
by
Haoyuan Liu
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful¯llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
May 2007
Copyright 2007 Haoyuan Liu
Object Description
| Title | On spectral approximations of stochastic partial differential equations driven by Poisson noise |
| Author | Liu, Haoyuan |
| Author email | haoyuanliu@hotmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2007-03-29 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-04-20 |
| Advisor (committee chair) | Mikulevicius, Remigijus |
| Advisor (committee member) |
Rozovskii, Lototsky, Sergey Vladimir Baxendale, Peter H. Ghanem, Roger Georges Zhang, Jianfeng |
| Abstract | In this dissertation, we will recall some basic settings and definitions for nonlinear filtering theory and based on the important optimal filtering estimator provided by Kallianpur, we will discuss the properties and equations which the 'unnormalized filtering density' (UFD) should satisfy. Lototsky, Mikulevicius and Rozovskii have done a great job in decomposing the UFD based on the Wiener Chaos Expansion theory and apply the theory numerically. We will derive a similar recursive numerical scheme with respect to the L2-CONS basis functions on the probabilistic space generated from the Poisson Point Measure and derive the growth rate of the error caused by the algorithm. Moreover, some alternative ways to reduce the error and making the algorithm more efficient are also going to be discussed. And definitely in the end, based on some numerical experiments from computer simulations, we will testify the validity and feasibility of our algorithm. |
| Keyword | stochastic partial differential equations |
| 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-m432 |
| Rights | Liu, Haoyuan |
| 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-Liu-20070420 |
| Archival file | uscthesesreloadpub_Volume48/etd-Liu-20070420.pdf |
Description
| Title | Page 1 |
| Full text | ON SPECTRAL APPROXIMATIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY POISSON NOISE by Haoyuan Liu A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful¯llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) May 2007 Copyright 2007 Haoyuan Liu |
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