On a Gauss-Kuzmin Type Problem for a Family of Continued Fractions

Abstract: We study a family of continued fraction expansion of reals from the unit interval. The Perron-Frobenius operator of the transformation which generates this expansion under the invariant measure of this transformation is given. Using the ergodic behavior of homogeneous random system with complete connections associated with this expansion we solve a variant of Gauss-Kuzmin problem for this continued fraction expansion.