Oberwolfach Seminar: The Ergodic Theory of Markov Processes
- October 24th - October 30th, 2010 (ID: 1043a)
- Martin Hairer, New York
- Jonathan Mattingly, Durham
- In recent years, much attention has been devoted to the study of stochastic partial differential equations (SPDEs)
that arise in a number of areas like turbulence, quantum field theory, material science, spatial models in epidemiology.
The solutions to such SPDEs form Markov processes, but on infinite-dimensional functional spaces.
Stochastic delay equations from another class of stochastic dynamics which also produces a Markov process
on an infinite dimensional space. While there are situations where the traditional tools of the theory of Markov processes
can be applied to such systems, they do fail in many important cases. This spurred a number of recent advances in the theory.
These have centered around the realization that the total variation metric, while very effective for countable state space Markov chains
and for finite-dimensional diffusion processes, is much less useful in the infinite dimensional setting.
The introduction of tools like asymptotic coupling and the asymptotic strong Feller property have lead to progress
on a number of problems which had been previously out of reach.
The aim of the proposed seminar is to provide young researchers with a grounding in these recent advances
as well as the foundations on which they are built. In addition, there will be a few advanced lectures on related topics.
- Prerequisites and Literature
- Participants are expected to be comfortable with measure theory, elementary stochastic analysis, functional analysis
and basic semigroup theory. For those wishing to refresh their memory on these subjects, we recommend the introductory chapters
of the following monographs:
Having a background in stochastic PDE theory will help but is not necessary to be able to follow the course.
A good introduction to the subject can be found in the monographs by Da Prato and Zabczyk,
"Stochastic equations in infinite dimensions" and "Ergodicity for infinite-dimensional systems".
A much shorter but reasonably self-contained introduction can be found online here:
An Introduction to Stochastic PDEs.
- "Measure Theory" by V.I. Bogachev,
- "Continuous Martingales and Brownian Motion" by D. Revuz and M. Yor,
- and "One- Parameter Semigroups" by B. Davies.
- Deadline for applications
- September 1st, 2010
The seminars take place at the
Mathematisches Forschungsinstitut Oberwolfach.
The number of participants is restricted to 25.
The Institute covers accommodation and food.
We are pleased that the Carl Friedrich von Siemens Foundation has decided
to support the Oberwolfach Seminars from summer 2008 to summer 2013.
By this support, travel expenses can be reimbursed up to 200 Euro in average per person.
Participants can ask for travel support during their stay in Oberwolfach at the guest office against copy of travel receipts.
- full name and address, including e-mail address
- present position, university
- name of supervisor of Ph.D. thesis
- a short summary of previous work and interest
should be sent preferably by e-mail (.ps or .pdf file) to:
Prof. Dr. Dr. h.c. Gert-Martin Greuel
67663 Kaiserslautern, Germany
Mathematisches Forschungsinstitut Oberwolfach
updated: June 8th, 2010