Universität Duisburg-Essen
Fakultät Mathematik, Campus Essen
Anita Winter

29th September 2017

Course (4SWS+2SWS)
Winter Semester 2015/16
Classes: Monday, 10.15-12.00 (S-U 3.03) and Wednesday 10.15-12.00 (S-U 3.03)
& Exercise Session: Wednesday 16.15-17.45 (S-U 3.03)

Probability Theory II


  1. Martingale Theory
  2. Filtrations; Stopping Times; Martingale, Sub- und Supermartingales; Predictability and Doob-Zerlegung; Optional Sampling; Optional Stopping; Martingale Convergence Theorems
  3. Weak convergence
  4. Portmanteau theorem, Helly's theorem, tightness, Prorohov's theorem, deFinetti's theorem
  5. Characteristic Functions und Laplace-Transforms
  6. Separable and convergence determining classes of functions
  7. Weak limit theorems
  8. Central Limit Theorem, Poisson Convergence
  9. Brownian Motion
  10. Stochastic Processes; Gaussian Processes; Construction of Brownian Motion; Strong Markov-Property and Reflection Principle; Law of iterated logarithm;
  11. Invariance principle
  12. Donsker's invariance principle; tightness Kolmogorov-Smirnov-statistics and the Brownian bridge

The course is for students with knowledge in measure theoretic probability (Wahrscheinlichkeitstheorie I)

Exercise sessions
The excercise sessions are tought by Tuan Anh Nguyen .

anita (dot) winter `at' due (dot)de