Measure theory, stochastic processes at the level of the course measure theoretic probability, see lecture notes https://staff.fnwi.uva.nl/s.g.cox/mtp_2016. 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 Itˆo 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 Bas kleijn (second half).