A Note on Rényi's 'Record' Problem and Engel's Series. Issue 2 (15th February 2018)

• Record Type: Journal Article
• Authors: Fang, Lulu; Wu, Min
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 61:Issue 2(2018)
• Page Start: 363
• Page End: 369
• Publication Date: 2018-02-15
• Subjects: large deviations, -- Markov processes, -- record times, -- Engel's series; Primary 60F10, -- 60J10, -- Secondary 62G30, -- 11A67; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091517000116
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: In 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.