AN INTRODUCTION TO STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Organized by

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): Stochastic 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

at

$[Department logo]$
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.

Programme:

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' equations
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.

Local organizers

For further information, please contact the local organizer Michael Sørensen.

CONCENTRATED ADVANCED COURSE: