Inhalt des Dokuments
A brief introduction to stochastic delay equations
We will give a brief introduction to stochastic delay equations driven by additive or multiplicative white noise. We will first discuss natural state spaces and the Markov property for solutions to such equations. We then continue to formulate relevant questions concerning the long time behavior of solutions like asymptotic stability in the sense of probability distributions. In particular we will mention the "coupling method" which has recently been developed to study invariant measures for Markov processes. We will try to keep the technical level low by explaining concepts and ideas rather that stating or proving mathematical theorems.