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