Examination for SDE (seminar course)

Compulsory home-works 1) Quadratic variation of Brownian Motion in L^2 (see ex. 2.17) 2) Construction of Ito integral : steps 1,2,3. 3) Ito isometry (proof of Lemma 3.1.5). Proof of elementary property of Ito integral (Th.3.2.1) and martingale property of the continous version ( Th.3.2.5 assumed) 4) Proof of the Ito formula. 4) Exercices: 4.11, 4.13, 4.14, 5.4, 5.7. A short seminar on one of the following topics -- Tanaka formula and local time (see also ex. 4.10) -- Ito's representation theorem (lemmas assumed done) and Martingale representation theorem. -- Markov property for Ito diffusions. -- Girsanov Theorem (with the possibility of referring to the book "Equazioni differenziali stocastiche e applicazioni" by P.Baldi).