# Stability and scaling limits for Markov processes and applications (1–3 cr)

**Lecturer**:

Prof Matthieu Jonckheere (U Buenos Aires)

**Schedule**:

Three lectures during 24–26 Sep 2018, every day 10:15–12:00 (Mon, Tue, Wed)

**Location**:

Krossi lounge (M220), 2nd floor, Otakaari 1, Aalto University

**Description**:

Markov processes allow to study models of almost any dynamics: population dynamics, data networks, physical systems evolutions, biological networks, etc. We will study techniques to answer stability questions including techniques allowing to link some Markov processes to simpler systems (often a deterministic dynamical system) via space-time scaling.

**Topics**:

1) Markov processes in discrete and continuous time

2) Stationary measures, reversibility

3) Martingales for Markov processes

4) Lyapunov functions

5) Scaling limits

6) Stochastic stability

**Evaluation**: You may get 1 cr for active participation at the lectures, and up to 3 cr by doing a project (to be agreed with the lecturer).

**Registration**: You can send an email to lasse.leskela@aalto.fi or just show up at the first lecture.