A CLT FOR THE L2 MODULUS OF CONTINUITY OF BROWNIAN LOCAL TIME

• 成果类型: Article
• 署名作者: Chen, Xia; Li, Wenbo V.; Marcus, Michael B.; Rosen, Jay
• 署名单位: University of Tennessee System; University of Tennessee Knoxville; City University of New York (CUNY) System; City College of New York (CUNY); University of Delaware; City University of New York (CUNY) System; College of Staten Island (CUNY)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP486
• 发表日期: 2010
• 页码: 396-438
• 关键词: l-p moduli; gaussian-processes; limit

摘要

Let {L-t(x); (x, t) is an element of R-1 x R-+(1)} denote the local time of Brownian motion, and alpha(t) := integral(infinity)(-infinity)(L-t(x))(2)dx. Let eta = N(0, 1) be independent of alpha(t). For each fixed t, integral(infinity)(-infinity)(L-t(x+h) - L-t(x))(2) dx - 4ht/h(3/2) L -> (64/3)(1/2) root alpha(t)eta as h -> 0. Equivalently, integral(infinity)(-infinity)(L-t(x+1) - L-t(x))(2) dx - 4t/t(3/4) L -> (64/3)(1/2) root alpha(1)eta as t -> infinity.