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 ...
Multivariate statistics focusses on inferring the joint distributional properties of several random variables, seen as random vectors, with a main emphasis on uncovering their underlying dependence structure. This course offers a broad introduction to its ...
Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented, including non-perturbative effects, such as tunneling an ...
Stochastic PDEs are used to model systems that are spatially extended and include a random component. This course gives an introduction to this topic, including some general measure theory, some Gaussian measure theory and some linear semigroup theory. ...
This is an introductory course to the concentration of measure phenomenon - random functions that depend on many random variables tend to be often close to constant functions. ...