Kolmogorov Type Law of the Logarithm for Arrays

Jørgen Hoffmann-Jørgensen (), Yu Miao (), Xiao Chun Li () and Shou Fang Xu ()
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Jørgen Hoffmann-Jørgensen: Aarhus University
Yu Miao: Henan Normal University
Xiao Chun Li: Henan Normal University
Shou Fang Xu: Xinxiang University

Journal of Theoretical Probability, 2016, vol. 29, issue 1, 32-47

Abstract: Abstract In this paper, we establish the analogue of Kolmogorov-type law of the logarithm for an array of independent random variables. The main methods are to develop the classic Bernstein’s and Kolmogorov’s inequality and replace the boundedness condition by conditions on the cumulant transform.

Keywords: Kolmogorov’s law of the logarithm; Independent random variables; Bernstein’s inequality; Kolmogorov’s inequality; 60F15 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-014-0574-8

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