Programme

Brownian motion: definition and property of BM, continuity and non-differentiability of the trajectories. Markov property, strong Markov property and reflection principle. Multi-dimensional BM, harmonic functions and Dirichlet problem. Skorokhod embedding and Donsker invariance principle.

Stochastic integration: Paley-Wiener-Zygmund integral. Stochastic integral, Ito's formula and applications. Stochastic differential equations, Theorem of existence and uniqueness of solutions of SDEs. Exercises.

Core Documentation

Brownian Motion (Moerters and Peres): http://www.mi.uni-koeln.de/~moerters/book/book.pdf

An introduction to Stochastic Differential Equations (Evans)

Type of delivery of the course

Some of the lectures are given by the lecturer and the others consist in presentations given by the students

Attendance

Presentations are given in the classroom (however there is the possibility to attend remotely)

Type of evaluation

Presentations as well as in-class participation. Part of the mark will depend on the exercises solved by the students.

Programme

Brownian motion: definition and property of BM, continuity and non-differentiability of the trajectories. Markov property, strong Markov property and reflection principle. Multi-dimensional BM, harmonic functions and Dirichlet problem. Skorokhod embedding and Donsker invariance principle.

Stochastic integration: Paley-Wiener-Zygmund integral. Stochastic integral, Ito's formula and applications. Stochastic differential equations, Theorem of existence and uniqueness of solutions of SDEs. Exercises.

Core Documentation

Brownian Motion (Moerters and Peres): http://www.mi.uni-koeln.de/~moerters/book/book.pdf

An introduction to Stochastic Differential Equations (Evans)

Type of delivery of the course

Some of the lectures are given by the lecturer and the others consist in presentations given by the students

Attendance

Presentations are given in the classroom (however there is the possibility to attend remotely)

Type of evaluation

Presentations as well as in-class participation. Part of the mark will depend on the exercises solved by the students.

Programme

Brownian motion: definition and property of BM, continuity and non-differentiability of the trajectories. Markov property, strong Markov property and reflection principle. Multi-dimensional BM, harmonic functions and Dirichlet problem. Skorokhod embedding and Donsker invariance principle.

Stochastic integration: Paley-Wiener-Zygmund integral. Stochastic integral, Ito's formula and applications. Stochastic differential equations, Theorem of existence and uniqueness of solutions of SDEs. Exercises.

Core Documentation

Brownian Motion (Moerters and Peres): http://www.mi.uni-koeln.de/~moerters/book/book.pdf

An introduction to Stochastic Differential Equations (Evans)

Type of delivery of the course

Some of the lectures are given by the lecturer and the others consist in presentations given by the students

Attendance

Presentations are given in the classroom (however there is the possibility to attend remotely)

Type of evaluation

Presentations as well as in-class participation. Part of the mark will depend on the exercises solved by the students.