Stochastic PDEs in terms of particle densities part.1
Event details
| Date | 27.04.2012 |
| Hour | 10:15 › 12:00 |
| Speaker | Carl Mueller |
| Location | |
| Category | Conferences - Seminars |
Probabilists have known for a long time that the solution of the heat equation can be viewed as the particle density of an infinite system of independent Brownian motions. If the particles undergo critical branching, we obtain the well known super-Brownian motion. This process is measure-valued, and it satisfies a stochastic partial differential equation (SPDE) in one dimension. In higher dimensions, it also satisfies an SPDE, but in the generalized sense. This process was one of the first examples of an SPDE related to a system of particles.
It turns out to be possible to view many SPDE in terms of particle densities. This viewpoint is not only suggestive, but has a rigorous formulation. In general, the particles will no longer be independent. But even so, we often have enough information to prove interesting results. Such results include blow-up, traveling waves, uniqueness and nonuniqueness, and even recent work on the KPZ equation.
In this mini-course, I will give the background for this approach and prove some of the most significant results.
It turns out to be possible to view many SPDE in terms of particle densities. This viewpoint is not only suggestive, but has a rigorous formulation. In general, the particles will no longer be independent. But even so, we often have enough information to prove interesting results. Such results include blow-up, traveling waves, uniqueness and nonuniqueness, and even recent work on the KPZ equation.
In this mini-course, I will give the background for this approach and prove some of the most significant results.
Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii