On the metrical theory of continued fraction mixing fibred systems and its application to Jacobi-Perron algorithm (Q1404219)

The authors study the metric theory of fibred systems in the case of continued fraction mixing systems. They obtain the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to the theorems for the regular continued fractions, obtained by \textit{J. Galambos} [Q. J. Math., Oxf. II. Ser. 23, 147-151 (1972; Zbl 0234.10041)], by \textit{W. Philipp} [Acta Arith. 28, 379-386 (1976; Zbl 0332.10033)] and by \textit{H. G. Diamond} and \textit{J. D. Vaaler} [Pac. J. Math. 122, 73-82 (1986; Zbl 0589.10056)]. These theorems hold for the Jacobi-Perron algorithm.