MATS256 Advanced Markov Processes (5 cr)

Open the course unit brochure on Sisu
Study level:
Advanced studies
Grading scale:
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.

Additional information

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
Grading scale:
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

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish

Teaching