Abstract
AbstractIn 1973, Williams [D. Williams, On Rényi's ‘record’ problem and Engel's series, Bull. London Math. Soc.5 (1973), 235–237] 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.
Publisher
Cambridge University Press (CUP)
Reference16 articles.
1. Théorie des éléments saillants d'une suite d'observations;Rényi;Ann. Fac. Sci. Univ. Clermont-Ferrand,1962
2. A new approach to the theory of Engel's series;Rényi;Ann. Univ. Sci. Budapest. Eötvös Sect. Math.,1962
3. On a joint strong approximation theorem for record and inter-record times
4. Precise asymptotics for record times and the associated counting process
5. Convergence rates for record times and the associated counting process
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