Special course “Nonlinear and nonlocal problems for partial differential equations and their applications”
10-12 lectures at 18:00 every Friday from February 17
Speakers: PhD A. V. Dymov, Doctor of Science S. B. Kuksin
Title of the talk: Random dynamical systems
The course is an introduction to the theory of random dynamical systems of the type to which differential equations with impulse random forces (known as “random kick forces”) lead. It will be explained that such systems are closely related to stochastic differential equations.
The main attention will be paid to the time-asymptotic properties of the trajectories of the systems. Namely, mixing criteria in such systems will be proved, it will be established that mixing entails the law of large numbers, and it will be discussed why mixing entails the central limit theorem. Most of the results will be obtained for systems in separable metric spaces, which will allow us to discuss the extension of the results to partial differential equations with random kick forces.