Topic outline

  • Materials

    • Lecture notes

      The main course material is the lecture notes. To pass the course with success requires you to study the lecture notes independently, because not everything that is is required in the exam will be discussed during the lectures. The lecture notes are subject to small updates during the course. The lecture notes are available both in English and in Finnish.

    • Additional online material

    • URL icon
      DA Levin, Y Peres: Markov Chains and Mixing Times URL

      Free online version of an excellent book by David Levin and Yuval Peres.

    • URL icon
      CM Grinstead, JM Snell: Introduction to Probability URL

      Free online version of a book by Grinstead and Snell.

    • Books

      An excellent book with emphasis on operations research and engineering applications is

      • VG Kulkarni. Modeling and Analysis of Stochastic Systems. Chapman and Hall/CRC 2016 (available online from Aalto library).

      A large portion of the topics discussed during the course are available for example in the textbooks

      • P Brémaud: Markov Chains, Springer 1999.
      • R Durrett. Essentials of Stochastic Processes. Springer 2012.

      If you are consider to study stochastics all the way up to MSc/DSc level, the following textbook might be recommended:

      • O Kallenberg: Foundations of Modern Probability. Springer 2002.

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