Glasnik Matematicki, Vol. 52, No. 2 (2017), 351-360.

THE DAVIS-GUT LAW FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED BANACH SPACE VALUED RANDOM ELEMENTS

Pingyan Chen, Mingyang Zhang and Andrew Rosalsky

Department of Mathematics, Jinan Unversity, Guangzhou, 510630, P. R. China
e-mail: zmy1021@qq.com

Department of Statistics, University of Florida, Gainesville, FL 32611, USA
e-mail: rosalsky@stat.ufl.edu

Abstract.   An analog of the Davis-Gut law for a sequence of independent and identically distributed Banach space valued random elements is obtained, which extends the result of Li and Rosalsky (A supplement to the Davis-Gut law. J. Math. Anal. Appl. 330 (2007), 1488-1493).

2010 Mathematics Subject Classification.   60F15.

Key words and phrases.   Davis-Gut law, law of the iterated logarithm, sequence of independent and identically distributed Banach space valued random elements.

DOI: 10.3336/gm.52.2.11

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