MATS256 Advanced Markov Processes (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
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
Completion methods
Course exam and exercises. Part of the exercises may be obligatory.
Final exam or oral exam are the other options.
Assessment details
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.
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.
* 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.
Additional information
The course is given every second year. It is given in 2017 and 2019.
Description of prerequisites
MATS352 Stochastic analysis or MATS353 Stochastic differential equations
Study materials
P. Protter. Stochastic Integration and Differential Equations
Jacod and Shiryaev. Limit Theorems for Stochastic Processes
Jacod and Shiryaev. Limit Theorems for Stochastic Processes
Completion methods
Method 1
Select all marked parts
Method 2
Select all marked parts
Parts of the completion methods
x
Unpublished assessment item
x
Unpublished assessment item