Random Continued fractions: Lévy constant and Chernoff-type estimate

Abstract

Given a stochastic process $\{A_n,n\ge 1\}$ taking values in natural numbers, the random continued fractions is defined as $[A_1,A_2,\cdots ,A_n,\cdots ]$ analogue to the continued fraction expansion of real numbers. Assume that $\{A_n,n\ge 1\}$ is ergodic and the expectation $E(\log A_1)<\infty$, we give a Lévy-type metric theorem which covers that of real case presented by Lévy in 1929. Moreover, a corresponding Chernoff-type estimate is obtained under the conditions $\{A_n,n\ge 1\}$ is $\psi$-mixing and for each $0<t<1$, $E(A_1^t)<\infty$.

18 pages

References in corpus (1)

• Large deviation principle for Benedicks-Carleson quadratic maps