University of Duisburg-Essen

Faculty of mathematics, Campus Essen

Prof. Martin Hutzenthaler (martin (dot) hutzenthaler 'at' due (dot) de)

März 2015

Lecture with exercises (2SWS+1SWS, 5ECTS)
in the
Summer term 2015

Lecture: Mondays 14.15-16.00 (room WSC-S-U-3.03)

Exercises: Mondays 16.15-17.00 (room WSC-S-U-3.03)

Lecture: Mondays 14.15-16.00 (room WSC-S-U-3.03)

Exercises: Mondays 16.15-17.00 (room WSC-S-U-3.03)

**Stochastic partial differential equations**

*Target audience:*

This lecture is an in-depth module stochastics (Vertiefungsmodul Stochastik)
for the master's programme (5ECTS).
The work load is about 150 hours (45 hours of presence time).

*Begin:*

The first lecture will be on Monday, April 13, 2015.
The exercises start on Monday, April 13, 2015.

*Content:*

- Infinite-dimensional stochastic integral definition and properties of the infinite-dimensional analog of Itô's lemma
- Stochastic partial differential equations Examples of second order SPDEs; strong, mild and weak solutions; existence, uniqueness and regularity of mild solutions; Martingale problems; Markov property
- Approximations of SPDEs Space, noise and time discretizations of SPDEs converging in the strong sense.

*Requirements:*

Students are required to be familiar with the lectures
'Wahrscheinlichkeitstheorie 1' and 'Wahrscheinlichkeitstheorie 2'
(or its contents, e.g., through Klenke's book 'Probability theory')
and are required to be familiar with the stochastic Itô's intgral, e.g.,
through the lecture 'stochastic differential equations'.

*Exercises:*

You will find all exercise sheets on the moodle course page.

*Moodle course:*

There is a
moodle course
on which everyone should
register. News and messages will be sent over this moodle platform.

*Exam:*

The exam will be on July 13, 2015 from 14:15-16 in room WSC-S-U-3.03

*Language:*

The language both in the lecture and in the exercises will be English
or - if preferred - German.

*Literature:*

- Prévot and Röckner: A concise course on stochastic partial differential equations 2007