  We present, in the simplest possible form, the so called martingale problem
strategy to establish limit theorems. The presentation is specially adapted to
problems arising in partially hyperbolic dynamical systems. We will discuss a
simple partially hyperbolic example with fast-slow variables and use the
martingale method to prove an averaging theorem and study fluctuations from the
average. The emphasis is on ideas rather than on results. Also, no effort
whatsoever is done to review the vast literature of the field.

Dynamical Systems