SoSe 21: Random Dynamical Systems
Maximilian Engel
Additional information / Pre-requisites
Prerequisites: An introductory course on Probability Theory; prior knowledge of Dynamical Systems/Ergodic Theory and Stochastic Processes/Stochastic Calculus is helpful but not necessary.
Comments
This course will give an overview how stochastic processes are seen from a viewpoint of dynamical systems theory. For deterministic systems that, for example, exhibit chaotic properties such that predictions for single trajectories are impossible, it is often very useful to make statements about the probability distribution of many trajectories. This observation is the basis of ergodic theory which focuses on probability distributions that stay invariant under the dynamics and correspond to asymptotic time averages of typical trajectories.
We will study systems where the randomness is part of the dynamics, for example in the form of stochastic differential equations, and discuss the connections to ergodic theory. Random dynamical systems is the mathematical theory for many real-world phenomena, such as synchronization or chaos, encountered in statistical and quantum physics, climate science, molecular dynamics, finance and economics and many others.
closeSuggested reading
L. Arnold, “Random Dynamical Systems”, Springer, 1998 (2nd printing, 2003).
P.D. Liu and M. Quian, “Smooth Ergodic Theory of Random Dynamical Systems”, Springer, 1995.
H. Crauel and P.E. Kloeden, “Nonautonomous and Random Attractors”, Jahresber Dtsch Math-Ver (2015) 117:173–206.
Z. Schuss, “Theory and Applications of Stochastic Processes. An Analytical Approach”, Springer, 2010. (One possible reference for background on Stochastic Processes and SDEs)
close14 Class schedule
Regular appointments