The course is an introduction to the theory of random dynamical systems such as those which correspond to differential equations with impulsive random forces (known as "random kick-forces"). It will be explained that such systems are closely related with stochastic differential equations. The main attention will be paid to the time-asymptotic properties of the trajectories of these systems. Namely, criteria for mixing in the systems will be obtained, it will be proved that mixing implies 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 make it possible to discuss their extension of to partial differential equations with random kick-forces.

Lecturers
Dymov Andrey Victorovich
Kuksin Sergei Borisovich

Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center