UNSPECIFIED. (1991) OPTIMAL STOPPING AND BEST CONSTANTS FOR DOOB-LIKE INEQUALITIES .1. THE CASE P = 1. ANNALS OF PROBABILITY, 19 (4). pp. 1798-1821. ISSN 0091-1798

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Abstract

This paper establishes the best constant c(q) appearing in inequalities of the form [GRAPHICS] where M is an arbitrary nonnegative submartingale and [GRAPHICS] The method of proof is via the Lagrangian for a version of the problem [GRAPHICS] where M = \B\, B a Brownian motion. More general inequalities of the form [GRAPHICS] and [GRAPHICS] (where parallel-to . parallel-to-phi and phi are, respectively, the Luxemburg norm and its dual, the Orlicz norm, associated with a Young function PHI) are established under suitable conditions on PHI. A simple proof of the John-Nirenberg inequality for martingales is given as an application.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ANNALS OF PROBABILITY
Publisher:	INST MATHEMATICAL STATISTICS
ISSN:	0091-1798
Date:	October 1991
Volume:	19
Number:	4
Number of Pages:	24
Page Range:	pp. 1798-1821
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/22351

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