The central limit theorem for random perturbations of rotations

Summary.   We prove a functional central limit theorem for stationary random sequences given by the transformations on the two-dimensional torus. This result is based on a functional central limit theorem for ergodic stationary martingale differences with values in a separable Hilbert space of square integrable functions. Received: 11 March 1997 / In revised form: 1 December 1997This research was supported by the Deutsche Forschungsgemeinschaft and the Russian Foundation for Basic Research, grant 96-01-00096. The second author was also partially supported by INTAS, grant 94-4194.