Diffusion Processes

What it is about

You will learn the mathematical theory of diffusion processes: Gaussian processes, stochastic integrals (Itô, Stratonovich, Klimontovich) and their transformation, Langevin equations to describe diffusions, and the analysis of diffusion operators using semigroup theory. You will also receive an introduction to log-Sobolev inequalities and to stochastic partial differential equations, so that you can formally analyze the models and treat them with semigroup-theoretic methods.

What you will be able to do

• Understand and apply Gaussian processes
• Master stochastic integrals (Itô, Stratonovich, Klimontovich)
• Analyze diffusion operators, in particular with semigroup methods
• Understand and apply logarithmic Sobolev inequalities
• Learn the fundamentals of stochastic partial differential equations

What the module consists of

• VorlesungProvision of theoretical foundations and examples; motivation for self-study
• ÜbungDiscussion of problem sheets for deepening and independent verification of learning success

Teaching method

• VorlesungIllustration of content with examples and discussion for motivation and systematic introduction
• Übungsgruppen / AufgabenblätterDeepening of methods and verification of understanding through working on and discussing problems