The lectures will be based on the lecture notes of Timo Seppalainen


Schedule see Mastermath website


Basic knowledge of real analysis, probability theory. Some knowledge of functional analysis is helpful.
Recommendend books on probability theory:
  • David Williams, Probability with Martingales
  • J. Michael Steele: Stochastic Calculus and Financial Applications
  • Kallenberg, Foundations of Modern probability (this is quite advanced)

  • Recommendend books on real analysis:
  • Rudin, Real Analysis
  • Aliprantis and Burkinshaw, Principles of real analysis
  • Measure theory, Fremlin, Measure theory volume 1.
  • A nice handout on measure theory and conditional expectations by Jan van Neerven

  • Recommendend books on functional analysis:
  • Bowers and Kalton, An Introductory Course in Functional Analysis
  • Coordinates

    see mastermath


  • Exercises till week 2
  • Selection of answers till week 1
  • Week 1: Introduction and Conditional expectations

  • Read chapter 1
  • For selection of exercises see the above file
  • Week 2: Filtrations stopping times and quadratic variation

  • Read sections 2.1 and 2.2 and bounded variation in chapter 1
  • For selection of exercises see the above file
  • Every measurable process which is adapted can be shown to have a version which is progressively measurable. Details can be found in Ondrejat and Seidler.
  • A good explanation of Dynkin's pi-lambda lemma can be found in David Williams book. The proofs are quite short.

  • More information on this course will no longer be put on this website but instead on wikispaces. Please send me an email with the request to be included if you want.