MATS254 Stochastic processes (4 cr)

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Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

The course gives an introduction into the theory of martingales and some applications. Martingales are one of
the most important classes of stochastic processes. They are widely used in stochastic modelling and in pure mathematics itself. The content of the course is:
  • martingales
  • Doob's optional stopping theorem
  • Doob's martingale convergence theorem
  • applications (Branching Processes and Kakutani's Dichotomy Theorem)

Learning outcomes

After completion of the course, the student
  • can calculate conditional expectations
  • can decide whether a stochastic process is a martingale
  • knows the basic conditions under which a martingale converges
  • can apply martingales in stochastic modelling

Description of prerequisites

MATA280 Foundations of stochastics

Recommended: Measure theoretic foundation of probability
(MATS260 Probability 1 or MATS112 Measure and Integration Theory 2)

Study materials

Lecture notes: S. Geiss. Stochastic processes in discrete time

Literature

  • D. Williams. Probability with martingales, 1991, Cambridge Mathematical Textbooks; ISBN: 978-0521406055

Completion methods

Method 1

Evaluation criteria:
The grade of the course is determined by the points aquired in the exam and in the exercises.
Time of teaching:
Period 2
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 (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English

Teaching

x

Exam (4 cr)

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

Teaching