# MATS256 Advanced Markov Processes (5 cr)

Study level:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

• 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

## Learning outcomes

The student
• knows Kolmogorov's existence theorem,
• knows about the main properties of strong Markov processes, Feller processes and Lévy processes,
• 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,
• learns to explain and present his/her own results to others and to discuss proofs from the course.

The course is given every second year. It is given in 2021 and 2023.

## Description of prerequisites

MATS352 Stochastic analysis or MATS353 Stochastic differential equations

## Study materials

J. Karatzas and S. Shreve. Brownian Motion and Stochastic Calculus

Sheng-wu He, Jia-gang Wang, Jia-An Yan, Semimartingale Theory and Stochastic Calculus,

## Completion methods

### Method 1

Evaluation criteria:
The grade of the course is determined by the points aquired in the exam and in the exercises.
Select all marked parts

### Method 2

Evaluation criteria:
The grade of the course is determined by the points aquired in the exam.
Select all marked parts
Parts of the completion methods
x

### Teaching (5 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
The grade for the course is based on the exam score and points aquired through the exercises.. At least half of the maximum score is required for passing..
Language:
English
No published teaching
x

Type:
Exam