A mini-course "Some chapters of the theory of stochastic differential equations (SDE)" by Professor Alexander Veretennikov
From February 28 to March 9, Professor of the University of Leeds (UK) and the leading research fellow of the International Laboratory of Stochastic Analysis and Its Applications (HSE, Russia) Alexander Veretennikov delivered a mini-course "Ergodic properties of Markov processes and the Poisson equation"
L1. A brief introduction to the theory of CDE. Strong and weak solutions. Random change of time. Invariant distributions. Stability of the SDE and convergence to the invariant distribution.
L2. Continuous analog of the MCMC method: the problem of construction of CDE with a given invariant distribution and the rate of convergence to this distribution. The problem and an example of the acceleration of convergence rate by means of a random change of time.L3-4. Stochastic Mckean - Vlasov equations. Existence, uniqueness and stationarity