Course content

The course gives an introduction to probability theory in a measure-theoretic setting. Among the topics discussed are: Probability measures, σ-algebras, conditional expectations, convergence of random variables, the law of large numbers, characteristic functions, the central limit theorem, filtrations and martingales in discrete time.

Learning outcome

After having completed the course

  • you know the measure-theoretic definitions of probability, independence, random variable, stochastic process, and conditional expectation
  • you know different ways to describe the distribution of a random variable
  • you know methods for treating and describing limits of sequences of random variables
  • you are familiar with how filtrations and conditional expectations are used