  We prove a central limit theorem for Birkhoff sums of the Rosen continued
fraction algorithm. A Lasota-Yorke bound is obtained for general
one-dimensional continued fractions with the bounded variation space, which
implies quasi-compactness of the transfer operator. The main result is a direct
proof of the existence of a spectral gap, assuming a certain behavior of the
transformation when iterated. This condition is explicitly proved for the Rosen
system. We conclude via well-known results of A. Broise that the central limit
theorem holds.
