Inhalt

• This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
  More precisely, the course will cover the following aspects of probability theory:
• Measure theory and the Lebesgue integral
• Convergence of random variables and 0-1 laws
• Generating functions: branching processes and characteristic functions
• Markov chains
• Introduction to martingales