Universität Duisburg-Essen
Fakultät Mathematik, Campus Essen
Anita Winter

2.October 2015

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


Content:

  1. Weak convergence
  2. Portmanteau theorem, Helly's theorem, tightness, Prorohov's theorem, deFinetti's theorem
  3. Characteristic Functions und Laplace-Transforms
  4. Separable and convergence determining classes of functions
  5. Weak limit theorems
  6. Central Limit Theorem, Poisson Convergence
  7. Martingale Theory
  8. Filtrations; Stopping Times; Martingale, Sub- und Supermartingales; Predictability and Doob-Zerlegung; Optional Sampling; Optional Stopping; Martingale Convergence Theorems
  9. Brownian Motion
  10. Stochastic Processes; Gaussian Processes; Construction of Brownian Motion; Strong Markov-Property and Reflection Principle; Increasing points of Brownian motion and random walk paths; Law of iterated logarithm; Skorohod-embedding und invariance principle; Kolmogorov-Smirnov-statistics and the Brownian bridge
  11. Introduction in stochastischen analysis
  12. Ito-integral; Ito-formula; weak and strong solutions of stochastic differential equations; existence and uniqueness theorem


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

Exercise sessions
The excercise sessions are supported by Wolfgang Löhr.

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

Literature:

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