Seminar: Reversible processes and the random walk on a *-graph

A discrete time, discrete state stationary process is said to be reversible if its law is invariant to time reversal. We introduce a random walk on a graph which represents several reversible models including Markov chains and processes with memory. We also introduce a reinforced version of the random walk which, due to de Finetti's theorem for Markov chains, defines a Bayesian predictive distribution for the aforementioned models. Applications to molecular dynamics will be discussed.