Large and moderate deviations for modified Engel series

ABSTRACT

The modified Engel series of real numbers introduced by Rényi (1962) is a simple modification of Engel series, and they have 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 studied the large and moderate deviations for modified Engel series, which indicate that the large deviations for modified Engel series and Engel series are different.

KEYWORDS:

• Large deviations
• moderate deviations
• modified Engel series.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 11A67
• Secondary 60F10

Acknowledgments

We wish to thank the referee for the helpful comments. The authors would also like to thank Dr Lulu Fang for mentioning this topic and sending them the papers Fang (2015a, b). This work was partially supported by the University Postgraduate Research and Innovation Project of Jiangsu Province (KYLX_150831).