CONTROL OF THE H-P NORM OF A MARTINGALE WITH THE MAXIMA OF LOCAL-TIMES

• 成果类型: Article
• 署名作者: LEURIDAN, C
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988184
• 发表日期: 1995
• 页码: 1289-1299
• 关键词: INEQUALITIES

摘要

Let B be a brownian motion starting at 0. We denote by L(t)(*) = max x is an element of R L(t)(*) the maximum of local times at time t. The Barlow-Yor inequalities tell us that for every p > 0, there are constants C-p > c(p) > 0 such that for every stopping time tau, c(p)E[tau(p/2)]less than or equal to E[L(tau)*(p)]less than or equal to C(p)E[tau(p/2)]. Given a fixed closed set F subset of R, we give a condition on F which is necessary and sufficient to derive similar inequalities with max(x is an element of F) L(tau)(x) instead of L(tau)(*) and we prove various related results.