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

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.

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