250068 VO Stochastic processes (2021W)

Stochastic processes describe the evolution of systems subject to randomness.
The simplest example of such systems are Markov chains, in which only information about the present state is retained for the future evolution.
Although these are simple to describe and arise in a large number of applications, there is a surprisingly rich theory describing the behaviour of such systems in the large time limit.

After discussing Markov chains in discrete time and discrete space, we will move on to the notion of martingale. This
fundamental concept plays the same role for stochastic processes that "constants of motion'' play in physics.