Stochastic Analysis
Academic year 2025/2026, first semester
Schedule
Weekly lessons: Monday, 10.30 to 12.15, and Friday, 8.30 to 10.15, always in Room 1BC50.
First meeting: Monday, 29 September 2025.
Bi-weekly exercise classes: Thursday, 16.30 to 18.15, Room 2BC60.
First meeting: 9 October 2025.
Program
- Motivation. Stochastic processes (basics). Recap on probability: notions of convergence, multivariate Gaussian distributions, conditional expectation.
- Brownian motion: construction and fundamental properties.
- Discrete and continuous time martingales.
- Stochastic integral: construction and properties.
- Itô calculus: Itô's formula, first applications (e.g. Dirichlet problem), Girsanov's theorem, martingale representation.
- Stochastic differential equations: notions of existence and uniqueness, fundamental theorem of existence and uniqueness, examples, Markov property and diffusions, Feynman-Kac formula.
Further Information
Please see the Moodle page.