We prove a functional central limit theorem for stationary random sequences given by the transformations Tε,ω(x,y) = (2x,y + ω + εx) mod 1 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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty