course

Last time (14. and 15. Feb.) 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 Ito?s Lemma (or Ito?s formula), which can be considered a chain rule for the Brownian motion and which is an important result in stochastic analysis (see Sect. 4 in ?ksendal). Next week (21. and 22. Feb.) 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).