Johel Beltrán (PUCP)

The Martingale problem is a concept introduced by Stroock and Varadhan
which can be understood as a sort of ordinary differential equation in
which the vector field is replaced by a field of second order
differential operators. A Markov process can be characterized as a
unique solution of a Martingale problem. This fact turns the
martingale problem in a very useful tool to prove convergence of
stochastic processes derived from Markov processes.

In this talk we shall use the martingale problem to prove the
convergence of processes arising in the study of metastable systems.
We shall explain how this tool is used in combination with other ones
like trace processes and potential theory. Finally, we shall show some
examples of systems in which this approach has been applied.

This is a joint work with C. Landim.

Department of Mathematics

Pontifical Catholic University of Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Center for Mathematical Modeling (CMM)

Faculty of Physical and Mathematical Sciences (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile