On the quenched central limit theorem for random dynamical systems

Journal Article

2016

Published in: On the quenched central limit theorem for random dynamical systems

We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure

• Volume Number: 49
• Issue Number: 24
• Magazine \ Newspaper: Journal of Physics A: Mathematical and Theoretical