Markov processes conditioned on large deviations
Hugo Touchette, National Institute for Theoretical Physics (NITheP),Stellenbosch, South Africa
I will discuss in this talk recent works with Raphael Chetrite (Université de Nice) on Markov processes conditioned on rare events – for example, Brownian motion conditioned on having a given asymptotic velocity or on staying positive for a very long time. I will show that a process conditioned on a large deviation can be represented in the long-time limit by a conditioning-free Markov process, called the driven or the equivalent process, which has the same typical states as the conditioned process. The driven process arises in the study of nonequilibrium processes and the simulation of large deviations. Other applications related to reaction paths, stochastic optimal control, and Brownian bridges and meanders will also be mentioned.