A note on Rényi's "record" problem and Engel's series

Abstract

In 1973, Williams introduced two interesting discrete Markov processes, namely $C$-processes and $A$-processes, which are related to record times in statistics and Engel's series in number theory respectively. Moreover, he showed that these two processes share the same classical limit theorems, such as the law of large numbers, central limit theorem and law of the iterated logarithm. In this paper, we consider the large deviations for these two Markov processes, which indicate that there is a difference between $C$-processes and $A$-processes in the context of large deviations.

7 pages. Some conclusions are added in this newest version

References in corpus (5)

• The large deviation approach to statistical mechanics
• Record occurrence and record values in daily and monthly temperatures
• Beta-expansion and continued fraction expansion of real numbers
• Large and moderate deviation principles for Engel continued fractions
• The denominators of convergents for continued fractions

Cited by in corpus (1)

• Large and moderate deviation principles for Engel continued fractions