This page was last updated May 3 11:21 1999
CONCENTRATED ADVANCED COURSE:
AN INTRODUCTION TO STOCHASTIC PARTIAL
Centre for Mathematical Physics and Stochastics
MaPhySto, which is funded by a
grant from The Danish National Research Foundation.
The lectures will be given by
PROFESSOR HELGE HOLDEN
from the Department of Mathematical Sciences, Norwegian University
of Science and Technology, Trondheim, Norway.
The course will be based on the book Holden, H., Øksendal, B.,
Ubøe, J. and Zhang, T. (1996):
Partial Differential Equations: A Modeling, White Noise
Functional Approach, Birkhauser.
Tutorial classes will be organized by FRED ESPEN
BENTH from the Department of Theoretical Statistics, University of Aarhus,
Denmark. Exercises: see
Miscellanea No. 6..
The course will take place in the period
SEPTEMBER 21-25, 1998
The Department of Theoretical Statistics
University of Copenhagen
The lectures will give a general introduction to stochastic
partial differential equations using white noise analysis.
In many applications that can be described by partial differential
equations, some of the parameters in the equation are not known
exactly. This may be due to lack of precise measurements or
incomplete knowledge of the processes involved. One can compensate
for this lack of information by replacing exact quantitive information
by qualitative information in terms of stochastic or random
parameters. In this setting white noise (formally the derivative of
Brownian motion) or functions thereof is introduced in various partial
differential equations as, e.g., a stochastic source term. In the white
noise approach white noise is defined rigorously as the fundamental object,
and Brownian motion is defined subsequently.
The equations we study will include the Poisson equation and the heat
equation with a stochastic source, the linear transport equation, the
Burgers' equations as well as the pressure equation.
Prerequisites: Background in stochastic analysis on the level of the
book by Øksendal (Stochastic Differential Equations, Springer 1998),
and general background in functional analysis.
September 21, 9:15-11:00: White noise analysis - the basics
September 22, 9:15-11:00: Stochastic distributions, the Wick product
September 23, 9:15-11:00: The Hermite transform and stochastic ODE's
September 24, 9:15-11:00: The stochastic Poisson, heat and Burgers'
September 25, 9:15-11:00: The stochastic pressure equation
There will be tutorial classes in the afternoons 13:15-15:00.
Lectures and tutorial
classes will take place in room E37 at Jagtvej.
For further information, please contact the