Ferienakademie 2023

Content

Stochastic evolution equations are random systems evolving in time. They have numerous applications, a recent example being so-called "stable diffusion", which is used to generate images, and classically noise driven processes in the natural sciences or in economics. An example for the latter is the Black-Scholes model for the dynamic of a financial  market with derivative investments.

In this course, we aim to explore the mathematical foundations of such equations. This course consists of two parts. The first half gives  an introduction to the mathematical foundations, such as Ito formula and martingales. The second part covers aspects of a solution theory, where we aim to cover recent work by Hoffmanova and Seidler, as well as numerical methods for stochastic differential equations (ordinary or partial, also depending on the participants' background and interest).