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.

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Facultad de Ciencias Físicas y Matemáticas (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile