Abstract. A new approach to the studies of statistical properties 
of hyperbolic dynamical systems (based on coupling method borrowed 
from probability theory) emerged recently; it was introduced by 
L.-S. Young and modified by D. Dolgopyat. We apply it here to 
Sinai billiards to derive a series of new results. First we 
establish sharp bounds on correlations (including multiple 
correlations). Then we use our correlation bounds to obtain the 
central limit theorem (CLT), the almost sure invariance principle 
(ASIP), the law of iterated logarithms, and integral tests.