forelesning/lesson

Last time (12., 13., 26. and 27. Sept.) we were concerned with the construction of the Ito integral with respect to the Brownian motion (see Sect. 3 in ?ksendal). In addition, we also discussed properties of such stochastic integrals (e.g. existence of a continuous version, martingale property,...) and Ito?s Lemma (or Ito?s formula), which can be considered a chain rule for the Brownian motion and which is a basic result in stochastic analysis (see Sect. 4 in ?ksendal). Next week (3. and 4. Oct.) we aim at proving the martingale representation theorem for (square integrable Brownian) martingales (sect. 4), which has many interesting applications (e.g. to stochastic control theory or mathematical finance). 

Problems to Exercises 3/Exercises 4 will be presented on Thursday, 4. Oct. (i.e. 1 hour lesson + 1 hour exercises).