The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mathematics. Moreover, the concepts of complete and incompl ...
This course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. The fundamental notions and techniques introduced in this course have many applications in finance, for example for option pricing, risk mana ...
In this course we will introduce and study numerical integrators for stochastic differential equations. These numerical methods are important for many applications. ...
This course introduces slow/fast systems and the mathematical tools used to derive effective equations governing their behaviour. Students will learn core concepts and techniques for rigorously analysing complex stochastic multi-scale systems. ...
Introduction to the mathematical theory of stochastic calculus: construction of the Ito stochastic integral, proof of the Ito formula, introduction to stochastic differential equations, Girsanov's theorem and the Feynman-Kac formula, the martingale represe ...
This course will provide a basic knowledge of the stochastic calculus of variations with respect to the Brownian motion. A variety of applications will be presented including the regularity of probability densities and quantitative normal approximations. ...
This course provides an in-depth treatment of the latest experimental and theoretical topics in quantum sciences and technologies, including for example quantum sensing, quantum optics, cold atoms, theory of quantum measurements and open dissipative quantu ...
In this lecture series some important objects of random geometry are introduced and studied. In particular, the relation between the Gaussian free field and random walks / Brownian motions is explored. This provides a toolbox of techniques for studying mat ...