Let Tε,ω be a transformation of the two-dimensional torus T2 given by the formula Tε,ω:(x, y) → (2x, y + ω + εx) mod 1. A version of the functional central limit theorem is formulated for variables of the form n-1/2 ∑k=0∞ f o Tε,ω k, where ε is an irrational number and f belongs to a class of real-valued functions on T2 described in terms of ε. The proof will be published elsewhere.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics