TY - JOUR

T1 - On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

AU - Nakada, Hitoshi

AU - Natsui, Rie

PY - 2003/4/1

Y1 - 2003/4/1

N2 - We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get 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 J. Galambos, W. Philipp, and H. G. Diamond-J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Petron algorithm.

AB - We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get 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 J. Galambos, W. Philipp, and H. G. Diamond-J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Petron algorithm.

KW - Continued fraction mixing

KW - Fibred system

KW - Jacobi-Perron algorithm

UR - http://www.scopus.com/inward/record.url?scp=0345060509&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345060509&partnerID=8YFLogxK

U2 - 10.1007/s00605-002-0473-4

DO - 10.1007/s00605-002-0473-4

M3 - Article

AN - SCOPUS:0345060509

SN - 0026-9255

VL - 138

SP - 267

EP - 288

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 4

ER -