Please note! Course description is confirmed for two academic years, 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 (valid 30.09.2020-21.12.2112):

Lecturer: Prof Lasse Leskelä (online office hours Mon 12–13 at Zoom)

Head assistant: Hoa Ngo (online office hours Tue 14.15-15.00 at Zoom)

Course assistants: Miro Lammi, Martti Ranta, Anton Vavilov

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

  • Applies in this implementation:

    The course grade g is determined by the exam and bonus points obtained from voluntary homeworks, online quizzes, and active participation according to formula:

      g = f(e+b2/3),

    where f is a monotone deterministic function, e = exam points (max 24), and b = bonus points (max 6). No bonus points are necessary for obtaining grade five. The bonus points are computed by

      b = (h + q/3 + 4a) / 12,

    where h = points from weekly homework problems (max 44), q = points from weekly online quizzes (max 48), and a = activity points (max 3). Activity points can be gathered from helping other students by asking helpful questions, answering others' questions, pointing out corrections to study materials etc. Attendance to lectures or exercise classes is voluntary and does not yield bonus points. Bonus points obtained during Autumn 2020 are valid in the exams of the academic year 2020–2021 which are held on:

    1. Wed 09 Dec 2020
    2. Wed 02 June 2021

  • 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.

  • Applies in this implementation:

    The primary reading material for the course is

    • L Leskelä: Stochastic processes, lecture notes (will be updated during the course)

    which is also available in Finnish. See Materials for more details and information about alternative study material.

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.


Details on the schedule
  • Applies in this implementation:

    Lectures: Mon 10–12 and Wed 10–12 at Zoom

    Exercise classes: Twice per week, five exercise groups, see WebOodi for details

    to register to the course and to an exercise group in WebOodi. For
    questions on practical matters concerning registering and exercises,
    contact the head assistant.