Journal article
Best Constants in Martingale Version of Rosenthal's Inequality
The Annals of probability, v 18(4), pp 1656-1668
01 Oct 1990
Abstract
The following generalization of Rosenthal's inequality was proved by Burkholder: A-1
p{|s(f)|p+ |d*|p} ≤ |f*|p≤ Bp{|s(f)|p+ |d*|p}, for all martingales (fn). It is known that Apgrows like$\sqrt{p}$as p → ∞. In this paper we prove that the growth rate of Bpas p → ∞ is p/ln p.
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Details
- Title
- Best Constants in Martingale Version of Rosenthal's Inequality
- Creators
- Pawel Hitczenko
- Publication Details
- The Annals of probability, v 18(4), pp 1656-1668
- Publisher
- Institute of Mathematical Statistics
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1990EH57900014
- Other Identifier
- 991020531817204721
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- Web of Science research areas
- Statistics & Probability