Probability and Stochastic Analysis - University of Bonn

Introduction to Stochastic Analysis WS 13/14

Prof. Dr. Anton Bovier

Time and location:Tuesdays,  8-10 We10/ Kleiner Hörsaal
Fridays,    10-12 We10/ Kleiner Hörsaal
Beginning:Tue. 14.10.2013


This course gives an introduction to the theory of stochastic analysis. 

The following key concepts are covered:

  • Brownian motion 
  • Continuous time martingales
  • Weak convergence and tightness
  • Stochastic integrals
  • Stochastic differential equations
  • Dirichlet problems 


The course builds on the lectures "Einführung in die Wahrscheinlichkeitstheorie" and "Stochastic processes". Lecture notes for both courses are available on my homepage. You are expected to have a reasonable knowledge of measure theory, know what conditional expectations are, have seen the construction of stochastic processes through the Daniell-Kolmogorov theorem, know key properties of martingales in discrete time, stopping times, and Markov processes. The cours is suitable for Bachelor students and as a foundations module for beginning Master students. 


A preliminary version of the lecture notes is available. There will be updates as we go along. For further reading, see the references given there.