MATJ5103 On recent developments on Markov Processes and Applications (JSS28) (2 op)
Osaamistavoitteet
The students are acquainted with basic and advanced parts of the theory of L'evy processes and self-similar Markov processes. They can deal with isotropic stable processes in high dimensions and are familiar with important path properties of these processes. The students are able to work on appropriate theoretical problems as well as on concrete examples.
Suoritustavat
Lectures, homework by solving problems
厂颈蝉盲濒迟枚
搂1. Quick review of Le虂vy processes
搂2. Stable processes seen as Le虂vy processes
搂3. Stable processes seen as a self-similar Markov process
搂4. Riesz鈥揃ogdan鈥揨ak transform
搂5. Hitting spheres
搂6. Spherical hitting distribution
搂7. Spherical entrance/exit distribution
搂8. Radial excursion theory
In this mini-course we will review some very recent work on isotropic stable processes in high dimension. The recent theory of self-similar Markov and Markov additive processes gives us new insights into their trajectories. Combining this with classical methods, we revisit some old results, as well as offering new ones.
Esitietovaatimukset
Some relatively basic knowledge of Levy processes, basic facts about Markov processes. Although pitched at the level of a graduate course, prerequisites are not significant beyond most undergraduate/masters level exposure to probability and stochastic processes.