Characterization of LIL behavior in Banach space

Abstract

In a recent paper by the authors a general result characterizing two-sided LIL behavior for real valued random variables has been established. In this paper, we show that there are analogous results in the Banach space setting. One of our main new tools is an improved Fuk-Nagaev type inequality in Banach space which should be of independent interest.

The Fuk-Nagaev inequality and he upper/ lower bound in Theorem 5 have been improved

References in corpus (2)

• Concentration around the mean for maxima of empirical processes
• Some results on two-sided LIL behavior