Almost sure invariance principle for some maps of an interval
- 1 December 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 5 (4) , 625-640
- https://doi.org/10.1017/s0143385700003217
Abstract
We prove an almost sure invariance principle and a central limit theorem for the process , where f is a map of an interval with a non-positive Schwarzian derivative whose trajectories of critical points stay far from the critical points, and F is a measurable function with bounded p-variation (p ≥ 1).The almost sure invariance principle implies the Log-log laws, integral tests and a distributional type of invariance principle for the process .Keywords
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