Measure theory, stochastic processes at the level of the course measure theoretic probability, see lecture notes pdf written by Peter Spreij.

Aim of the course

  • The students can explain the theory and construction of stochastic integrals,
  • the students are able to apply the Ito formula,
  • the students can explain different solution concepts of SDEs, students know how to apply measure changes for continuous semimartingales (Girsanov's theorem) and are able to calculate the new drift,
  • the students are able to compare SDEs and PDEs, and can calculate the probabilistic representation of solutions to PDEs,
  • the students are able to solve problems, where knowledge of the above top ics is essential.

Asma Khedher (first half) and Gergely Bodo (second half)