Characterization of LIL behavior in Banach space

2006/08/28 by Uwe Einmahl, Einmahl, Uwe, Deli Li +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60B12 #60F15 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications #math.PR #msc:60B12 #msc:60F15

paper · pdf · doi:10.48550/arxiv.math/0608687

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

openalex publication_date 2006/08/28 · arxiv created 2007/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Fuk-Nagaev inequality in smooth Banach spaces: Optimum bounds for distributions of heavy-tailed martingales

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