OPTIMAL STOPPING AND BEST CONSTANTS FOR DOOB-LIKE INEQUALITIES .1. THE CASE P = 1
成果类型：
Article
署名作者：
JACKA, SD
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990237
发表日期：
1991
页码：
1798-1821
关键词：
摘要：
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.