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OPTIMAL STOPPING AND BEST CONSTANTS FOR DOOB-LIKE INEQUALITIES .1. THE CASE P = 1

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

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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
Official Date: October 1991
Dates:
DateEvent
October 1991UNSPECIFIED
Volume: 19
Number: 4
Number of Pages: 24
Page Range: pp. 1798-1821
Publication Status: Published

Data sourced from Thomson Reuters' Web of Knowledge

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