MS-E1600 - Probability Theory D, Lecture, 8.1.2024-19.2.2024

Topic outline

• Materials
  The main course material is the lecture notes:

  • K Kytölä. Probability Theory. Aalto University 2019.

  
  

  Additional useful learning materials are provided in the pdf files below.  They contain more details about probability density functions, probability kernels, probability metrics, and so on.

  
  

  • Select activity Additional reading

    Additional reading

  • Select activity Order, topology, and sigma-algebras on the extended real line

    

    Order, topology, and sigma-algebras on the extended real line File PDF

    Completion

    Students must

    

    View
  • Select activity Weighted measures and densities

    

    Weighted measures and densities File PDF

    Completion

    Students must

    

    View
  • Select activity Probability metrics

    

    Probability metrics File PDF

    Completion

    Students must

    

    View
  • Select activity TextbooksFor those who prefer to read a standard t...

    Textbooks

    For those who prefer to read a standard textbook instead, one option is the official course textbook

    • J Jacod & P Protter. Probability Essentials. Springer 2004.

    
    Another textbook, with essentially the same contents compressed into a smaller number of pages, is
    

    • D Williams. Probability with Martingales. Cambridge University Press 1991.

    
    

    If you are planning to continue your studies in probability further, possibly to a doctoral level, a recommended option is to consider the following reference book which contains a vast amount of content:

    • O Kallenberg. Foundations of Modern Probability. 3rd edition. Springer 2021.

    
    

  • Select activity Old lecture videosOld lecture videos from the cour...

    Old lecture videos

    Old lecture videos from the course Spring 2021 are available at https://youtube.com/playlist?list=PLLUr70a-tqjf5htSOg4qeFCx-jqM2jlO5.