MS-E1991 - Brownian motion and stochastic analysis, 14.04.2020-22.05.2020

Materials

• Materials
  

  Materials

  Literature

  
  

  Textbooks:

  Main textbook:
  

  • Le Gall, J.-F. Brownian Motion, Martingales, and Stochastic Calculus. Graduate Texts in Mathematics, volume 274, 2016.
    

  Alternative textbook:
  

  • Durrett, R. Stochastic calculus: a practical introduction. CRC  Press, Probability  and Stochastics Series, 1996.
    

  Freely available online notes corresponding roughly to the course contents:
  

  • Berestycki, N. Stochastic calculus.

  
  

  Older lecture notes:

  Lecture notes from a course in 2017-2018:

  • lecture notes
    

  
  

  Background material:

  We assume familiarity with probability theory. Suitable background material for this includes:
  

  • Kytölä, K. Lecture notes for the course MS-E1600 Probability theory.
    
  • Durrett, R. Probability: theory and examples. Cambridge University Press, 2010.
    
  • Williams, D. Probability with martingales. Cambridge University Press, 1991.
    

  The main textbooks for the course also assume familiarity with discrete time martingale theory. The last two of the above references also cover background on this.