Valentin Rapenne

In probability theory, mathematicians often get random variables as limit objects of some stochastic processes. For example, this situation is very common when we are able to identify a martingale. A natural question is to know the probability distribution of this limit random variable. However we can also ask ourselves the reverse question: Is it possible to describe the whole stochastic process thanks to the probability distribution of this limit random variable? We will see that this is possible in a particular setting called "exchangeability" thanks to a theorem of De Finetti. We will try to apply it on a simple and well-known example called the "Polya's urn". Finally we will see how exchangeability can be used to study a far more complicated stochastic process: the edge reinforced random walk.