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Using the natural extension forθ-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the previous fraction expansion.doi:10.1155/2014/980461 fatcat:ei3hbs2fenbedlb5ql5qgx2isu