The central limit theorem for random perturbations of rotations |
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Authors: | Manfred Denker Mikhail Gordin |
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Affiliation: | Institut für Mathematische Stochastik, Universit?t G?ttingen, Lotzestr. 13, D-37083 G?ttingen, Germany. e-mail: denker@namu01.gwdg.de, DE St. Petersburg Division of V.A. Steklov Mathematical Institute, Fontanka 27, 197011 St. Petersburg, Russia. e-mail: gordin@pdmi.ras.ru, RU
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Abstract: | 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. |
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Keywords: | Mathematics Subject Classification (1991): 60F05 28D05 58F11 |
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