THE STUDY OF ITO-CLIFFORD STOCHASTIC INTEGRALS AND STOCHASTIC DIFFERENTIAL EQUATIONS
THE STUDY OF ITO-CLIFFORD STOCHASTIC INTEGRALS AND STOCHASTIC DIFFERENTIAL EQUATIONS
No Thumbnail Available
Date
2010-07
Authors
YUSUF, AHMED OMEIZA
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In this thesis we review an integral of anti-commuting elements analogous to the Itointcgral
for Brownian motion.
We will also extend the stochastic integral to a wider class of integrands. The extension
was achieved by using the inequalities in Remark 4.11 of chapter four.
Similarly we will also shown that a stochastic differential equation of the form
dXt
=F(Xt't)dWt+dWtG(Xt't)+H(Xt't)dt has a unique solution in the L2
-space of
Clifford algebra for any initial condition provided that F,G,H satisfy a Lipschitz
condition.
Description
A THESIS SUBMITTED TO THE POST GRADUATE SCHOOL,
AHMADU BELLO UNIVERSITY, ZARIA NIGERIA
IN PARTIAL FULFILMENT FOR THE AWARD OF DEGREE OF
MASTER OF SCIENCE DEGREE IN MATHEMATICS
DEPARTMENT OF MATHEMATICS AHMADU BELLO
UNIVERSITY, ZARIA NIGERIA
JULY, 2010
Keywords
ITO-CLIFFORD,, STOCAHSTIC INTEGRALS,, STOCHASTIC,, EQUATIONS