Pierre Collet (Ecole Polytechnique)

Title:  Quasi stationary distributions (q.s.d.) for stochastic processes and dynamical systems.


Assume the phase space (space of states) of a stochastic process or a dynamical system has a hole. We are interested in the trajectories which have not reached the hole up to time T. What can be said about the distribution of these survivors at time T ? Is there a limit when T tends to infinity ?

The course will be (tentatively) organized as follows

I) Simple examples (Markov chains with finite state space, dynamical systems). General definitions and properties, q.s.d., Yaglom limit.

II) Diffusions, examples from population dynamics.

III) Gibbs states,  Pianigiani Yorke measures.