D. Volny, Universite de Rouen, France

Abstract:
When studying limit theorems for stationary non independent processes, martingale approximation has been a powerful tool. It was, however, supposed to be an exclusively one dimensional thing.
One of stumbling blocks has been that for an ergodic field of martingale differences the CLT does not hold.
In last five years several paper a substantial progress appeared. In particular it has been proved that for martingale differences (in the sense of Khosnevisan) the partial sums converge always but even in ergodic case the limit law need not be normal.