Time and location of the lecture course:

Wednesday 11:00-13:00 (c.t.) and Friday 09:30-11:00

Institut für Angewandte Mathematik, MΛTHEMΛTIKON, INF205, SR B (Wed) and SR 5 (Fri)

Contact:

Lecturer: Prof. Dr. Jan JOHANNES <johannes[at]math.uni-heidelberg.de>

Exercise instructor: Maximilian Nitzschner <nitzschner.maximilian.alexander[at]web.de>

Questions, please directly by email or by using the contact form.

Language:

The lecture courses and the exercises will be hold in English
if there is at least one non-German speaking participant.
Otherwise the teaching will be in German.

Content of the lecture course:

• Preliminaries
  • Basic measure theory, Random variables, Independence,
  • Expectation, Convergence of random variables, Conditional expectation
• Stochastic processes
  • Probability measures on Polish spaces,
  • Adapted processes and stopping time
• Martingale theory
  • Martingales, sub- and supermartingales,
  • Martingale inequalities and convergence
• Markov chains
  • Recurrence, Transience
• Ergodic theory
  • Stationary and ergodic processes, Ergodic theorems
• Weak convergence
  • Fundamental properties, Tightness
• Brownian Motion
  • Existence, Donsker’s theorem, Markov properties,
  • Stochastic integrals, Itô rule