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.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
Denker, M., Gordin, M. The central limit theorem for random perturbations of rotations. Probab Theory Relat Fields 111, 1–16 (1998). https://doi.org/10.1007/s004400050160
Issue Date:
DOI: https://doi.org/10.1007/s004400050160
- Mathematics Subject Classification (1991): 60F05
- 28D05
- 58F11