Pensum/Syllabus

Course books:

1. Bernt ?ksendal: Stochastic Differential Equations, 2013. Springer. (6th Edition Corrected Printing).

2. Cohen, S. N., Elliott, R. J.: Stochastic Calculus and Applications. Birkh?user, 2nd edition (2015).

3. Chung, K.L., Williams, R. J.: Introduction to Stochastic Integration. Birkh?user, 2nd edition (2013). 

Chapters in the corresponding books:

1. Definition of stochastic integrals with respect to integrators given by right continuous local martingales (see Ch. 2, 3 in Chung, Williams or Ch. 12 in Cohen, Elliot). Discussion of stochastic integrals with respect to the Brownian motion (see Ch. 3 in ?ksendal).

2. Ito-formula and martingale representation theorem with respect to the Brownian motion (see Ch. 4 in ?ksendal)

3. Stochastic differential equations driven by Brownian motion (Existence/Uniqueness of strong and weak solutions). See Ch. 5 in the book of ?ksendal.

4. Linear filtering theory, if time permits. See Ch. 6 in ?ksendal.

5. Diffusions: Basic properties: Discussion of e.g. the Markov property of diffusions or Dynkin?s formula. See Ch. 7 in ?ksendal.

6. Other topics in diffusion theory: E.g. Kolmogorov?s backward equation, Feynman-Kac formula, Girsanov?s theorem (Ch. 8 in ?ksendal or Ch. 15, 17 in Cohen, Elliot).

7. Applicatons to boundary value problems: E.g. discussion of the combined Dirichlet-Poisson problem (Ch. 9 in ?ksendal).

8. Application to stochastic control: HMB equation (see Ch. 11 in ?ksendal or Ch. 21 in Cohen, Elliot).