Details

Autor(en) / Beteiligte

• Klass, Michael J.
• Nowicki, Krzysztof

Titel

An Improvement of Hoffmann-Jorgensen's Inequality

Ist Teil von

• The Annals of probability, 2000-04, Vol.28 (2), p.851-862

Ort / Verlag

Hayward, CA: Institute of Mathematical Statistics

Erscheinungsjahr

2000

Link zum Volltext

Quelle

Elektronische Zeitschriftenbibliothek

Beschreibungen/Notizen

• Let B be a Banach space and F any family of bounded linear functionals on B of norm at most one. For x ∈ B set || x || = supΛ∈FΛ (x) (||· || is at least a seminorm on B). We give probability estimates for the tail probability of S* n= max1≤ k≤ n||Σk j=1Xj|| where {Xi}n i=1are independent symmetric Banach space valued random elements. Our method is based on approximating the probability that S* nexceeds a threshold defined in terms of Σk j=1Y(j), where Y(r)denotes the rth largest term of {|| Xi||}n i=1. Using these tail estimates, essentially all the known results concerning the order of magnitude or finiteness of quantities such as EΦ(|| Sn||) and EΦ(S* n) follow (for any fixed 1 ≤ n ≤ ∞). Included in this paper are uniform Lpbounds of S* nwhich are within a factor of 4 for all p ≥ 1 and within a factor of 2 in the limit as p → ∞.