Course description
Markov processes are random functions of time whose past and future are conditionally independent, given their present. As such, they are widely used to model complex random evolutions in our physical world, and serve as efficient stochastic algorithms for the exploration of massive networks or the generation of random high-dimensional data. The aim of this course is to provide an introduction to their general theory, with an emphasis on examples and applications. We will cover the following notions:
- Discrete-time Markov chains
- Pure jump processes
- Markov diffusions
- Convergence to equilibrium