Topic outline

  • General

    This course will get you introduced to stochastic processes, the theory of time-dependent random phenomena. You learn to mathematically model and analyze particle and population flows using Markov processes, unpredictable time instants using Poisson processes, and gambling and investment strategies using martingales.

    What are Stochastic Processes about? Check out the 15min introductory video by Lasse Leskelä (start at time 03:20 in the video link)!

    See the course syllabus for details on schedules, grading, and other arrangements.


    In brief, the course comprises the following activities:

    • lectures (optional): 2 times/week
    • exercise classes (optional): 2 times/week
    • homework problems (handed in and graded, optional but can contribute significantly to the grade): due 2 times/week
    • quizzes in MyCourses (optional, give bonus points): 2 times/week; except only once in the first lecture week
    • written exam (in the end of the course, on 7th December)

    The course can be passed in two ways (the option that gives the better grade will be implicitly chosen for you):

    • Via written exam + handed-in homework (both affect the grade, exam 60% and homework 40%); you can gain bonus points from the in-person exercise classes and online quizzes.

    • Via written exam only (100% grade from exam points).


    Grading will be performed as follows, using a monotone deterministic function f:

    • Passing via written exam + handed-in homework: The grade is determined by the formula f(3e/5 + 12h/55 + (b/10)^{2/3}) where e are the points from the exam (max. 24p), h are the points from the returned homework (max. 44p), and b = q + c are the bonus points, where q are the points from the online quizzes (max. 33p) and c are the points from the classroom exercises (max. 11p). 
    • Passing via written exam only: The grade is determined by the formula f(e), where e are the points from the exam (max. 24p).

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