Page 1 |
Save page Remove page | Previous | 1 of 118 | Next |
|
small (250x250 max)
medium (500x500 max)
large ( > 500x500)
Full Resolution
All (PDF)
|
This page
All
Subset |
NUMERICAL WEAK APPROXIMATION OF
STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY L EVY PROCESSES
by
Changyong Zhang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
December 2010
Copyright 2010 Changyong Zhang
Object Description
| Title | Numerical weak approximation of stochastic differential equations driven by Levy processes |
| Author | Zhang, Changyong |
| Author email | changyoz@usc.edu; changyoz@yahoo.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date submitted | 2010 |
| Restricted until | Unrestricted |
| Date published | 2010-11-22 |
| Advisor (committee chair) | Mikulevicius, Remigijus |
| Advisor (committee member) |
Lototsky, Sergey Zhang, Jianfeng Ghanem, Roger |
| Abstract | Levy processes are the simplest generic class of processes having a.s. continuous paths interspersed with jumps of arbitrary sizes occurring at random times, which makes them useful tools in a variety of fields including mathematics, physics, engineering, and finance.; In stochastic analysis, it is frequently necessary to evaluate functionals of the process modeling the system of interest. In general, the law of the process is unknown and a closed-form solution is unrealistic. An alternative possibility is to numerically approximate the functionals by discrete time Monte-Carlo simulation, which is widely applied in practice. The simplest scheme for Monte-Carlo simulation is the weak Euler approximation. In such numerical treatment of stochastic differential equations, it is of theoretical and practical importance to estimate the rate of convergence of the discrete time approximation.; In this dissertation, the weak Euler approximation for stochastic differential equations driven by Levy processes is studied. The model under consideration is in a more general form but with weaker assumptions than those in existence. Hence, it is applicable to a broader range of processes arising from various fields. In order to investigate the convergence of the weak Euler approximation to the process considered, the existence of a unique solution to the corresponding integro-differential equation in Holder space is first proved. It is then identified that the Euler scheme yields a positive weak order of convergence, provided that the coefficients of the stochastic differential equation are Holder-continuous and the test function is continuously differentiable to some positive order. In particular, if the coefficients are slightly more than twice differentiable and the test function has up to the fourth order derivative, then first weak order convergence is guaranteed. |
| Keyword | weak Euler approximation; rate of convergence; stochastic differential equations; Levy processes; Nondegenerate; Holder continuity |
| 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-m3547 |
| Rights | Zhang, Changyong |
| 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-Zhang-3943 |
| Archival file | uscthesesreloadpub_Volume40/etd-Zhang-3943.pdf |
Description
| Title | Page 1 |
| Full text | NUMERICAL WEAK APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY L EVY PROCESSES by Changyong Zhang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) December 2010 Copyright 2010 Changyong Zhang |
Comments
Post a Comment for Page 1
