DIFFERENTIAL SUBORDINATION AND STRONG DIFFERENTIAL SUBORDINATION FOR CONTINUOUS-TIME MARTINGALES AND RELATED SHARP INEQUALITIES

• 成果类型: Article
• 署名作者: WANG, G
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988278
• 发表日期: 1995
• 页码: 522-551
• 关键词: Transforms; INTEGRALS

摘要

Let X and Y be two continuous-time martingales. If quadratic variation of X minus that of Y is a nondecreasing and nonnegative function of time, we say that Y is differentially subordinate to X and prove that \\Y\\(p) less than or equal to (p* - 1)\\X\\(p) for 1 < p < infinity, where p* = p boolean OR q and q is the conjugate of p. This inequality contains Burkholder's L(p)-inequality for stochastic integrals, which implies that the above inequality is sharp. We also extend his concept, of strong differential subordination and several other of his inequalities, and sharpen an inequality of Banuelos.