Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


Upon completing the course, the student

1. is familiar with the most common types of stochastic processes used in the modeling of random phenomena, and is aware of their underlying assumptions,

2. can apply stochastic processes to modeling and analyzing random phenomena,

3. is prepared to extend his/her knowledge to more sophisticated models, for example using the scientific literature in the field.

Credits: 5

Schedule: 26.10.2020 - 09.12.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Lasse Leskelä

Teacher in charge (applies in this implementation): Lasse Leskelä

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    Random vectors and random processes. Markov chains. Branching processes. Random point patterns and Poisson processes. Population models, queues, and gambling.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Exam and voluntary homework

  • Valid 01.08.2020-31.07.2022:

    Attending lectures 24 h (4)
    Attending exercise classes 24 h (4)
    Attending and preparing for the exam 2-32 h
    Weekly independent study 50-80 h


Study Material
  • Valid 01.08.2020-31.07.2022:

    • L Leskelä. Stochastic processes. Lectures notes 2019.
    • DA Levin, Y Peres. Markov Chains and Mixing Times. American Mathematical Society 2017.
    • P Brémaud: Markov Chains, Springer 1999.
    • VG Kulkarni. Modeling and Analysis of Stochastic Systems. Chapman and Hall/CRC 2016.

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Mat-2.3111 Stochastic Processes

  • Valid 01.08.2020-31.07.2022:

    MS-A05XX First course in probability and statistics, MS-A000X Matrix algebra and MS-A02XX Differential and integral calculus 2 or equivalent knowledge.



Registration and further information