MATS256 Advanced Markov Processes (5 cr)
Learning outcomes
* the student knows Kolmogorov's existence theorem
* the student knows about the main properties of strong Markov processes, Feller processes and Lévy processes
* the student understands the different approaches of certain classes of Markov processes and the benefits from that, for example how to construct weak solutions to stochastic differential equations.
Study methods
Course exam and exercises. Part of the exercises may be obligatory.
Final exam or oral exam are the other options.
Content
* existence of Markov processes,
* strong Markov processes,
* different approaches of certain classes of Markov processes: semigroup, infinitesimal generator, martingale problem, Dirichlet form, stochastic differential equation,
* Feller processes,
* Lévy processes
Further information
The course is given every second year. It is given in 2017 and 2019.
Materials
P. Protter. Stochastic Integration and Differential Equations
Jacod and Shiryaev. Limit Theorems for Stochastic Processes
Assessment criteria
The grade is based on
a) the number of points in the course exam and possibly additional points from exercises
OR
b) the number of points in the final exam.
At least half of the points are needed to pass the course.
Prerequisites
MATS352 Stochastic analysis or MATS353 Stochastic differential equations