After successful completion of the course, students are able to...
interpret and do computations with stochastic integrals; - give proof of well-posedness of stochastic differential equations; - analyze and implement basic numerical algorithms for the simulation of solutions.
Brownian motion. Stochastic calculus. Ito's formula. Existence and uniqueness theory. Girsanov transformation. Euler-Maruyama scheme. Weak and strong rates of convergence.
Online lectures and exercises (in the companion UE course). In the lecture the theory is introduced and examples will be calculated. Once a week there will be exercise-sheets which will be calculated at by the students in an interactive online session.
Oral exam
Not necessary
Basic probability theory, Ordinary differential equations