Mini-course “Ergodic properties of Markov processes and Poisson equations”

The goal of the course is to introduce to the area of ergodic properties of Markov chains and processes in discrete and continuous time starting from a very classical ergodic theorem for finite Markov chains and finishing by Poisson equations with a potential and by further applications of Poisson equations. The approximate syllabus of six lectures – each of them four academic hours long – in September 2016 is as follows. Each item approximately corresponds to one slot of four hours lecture.

(1) Ergodic theorem(s) & Law of Large Numbers for Markov processes.

(2) Central Limit Theorem for Markov processes.

(3) Large deviation (LD) inequalities and LD asymptotics for Markov processes.

(4) Poisson equation with boundary conditions and without boundary conditions.

(5) Applications of Poisson equations to (Functional) Central Limit Theorems.

(6) Poisson equations with a potential.

The main source for studies will be the lectures and lecture notes (in preparation). An additional recommended literature (further articles may be added later):

1. A.A. Borovkov, Probability theory (any edition and year, e.g., Springer, London, 2013).

2. E. Pardoux & A.Yu. Veretennikov, On the Poisson equation and diffusion approximation, 1. Annals of Probability, 2001, 29(3), 1061-1085; DOI 10.1214/aop/1015345596

Schedule of mini-course:
 06, 08, 13, 15, 22, 24 September 2016, 18.10-21.00, Shabalovka, 26, room 5408.

Course is open to anyone interested. Whether you need the pass to the Higher School of Economics, do not hesitate  to contact Anna Kozhina <annaakozhina@gmail.com>.