Limit theorems for sums of partial quotients of continued fractions

DOI10.1007/BF01636928zbMath0638.60039MaRDI QIDQ1099487

Walter Philipp

Publication date: 1988

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178375

zbMATH Keywords

strong law of large numberscentral limit theoremcontinued fraction expansiondomain of normal attraction to a stable law

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Metric theory of continued fractions (11K50)

Related Items (25)

On the extremal theory of continued fractions ⋮ Quantitative metric theory of continued fractions ⋮ On the local times of stationary processes with conditional local limit theorems ⋮ Big Birkhoff sums in $d$-decaying Gauss like iterated function systems ⋮ Limit theorems for sub-sums of partial quotients of continued fractions ⋮ Partial sum processes and continued fractions ⋮ On the local limit theorems for psi-mixing Markov chains ⋮ The distribution of the large partial quotients in continued fraction expansions ⋮ On the Product of Random Variables and Moments of Sums Under Dependence ⋮ Prime numbers in typical continued fraction expansions ⋮ Metrical properties of the large products of partial quotients in continued fractions ⋮ On sums of partial quotients in Hurwitz continued fraction expansions ⋮ Marcinkiewicz laws with infinite moments ⋮ Lochs-type theorems beyond positive entropy ⋮ A distributional limit law for the continued fraction digit sum ⋮ Full dimensional sets of reals whose sums of partial quotients increase in certain speed ⋮ Subexponentially increasing sums of partial quotients in continued fraction expansions ⋮ Large deviation principle for arithmetic functions in continued fraction expansion ⋮ On limit theorems for continued fractions ⋮ Limit theorems for counting large continued fraction digits ⋮ On Kolmogorov’s converse inequality for dependent random variables ⋮ Limit theorems for sums of products of consecutive partial quotients of continued fractions ⋮ Random continued fractions: Lévy constant and Chernoff-type estimate ⋮ ON THE LARGEST PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS ⋮ On Some Limit Theorems for Continued Fractions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of sums of mixing triangular arrays of random vectors with stationary rows
• Estimates for partial sums of continued fraction partial quotients
• Asymptotic normality of trimmed sums of \(\Phi\)-mixing random variables
• Universal asymptotic normality for conditionally trimmed sums
• Maße, die von regelmäßigen Kettenbrüchen induziert sind
• Some metrical theorems in number theory. II. - Errata
• Fractions continues aléatoires
• Über Einen Kusminschen Satz
• The central limit problem for mixing sequences of random variables

This page was built for publication: Limit theorems for sums of partial quotients of continued fractions