Lower tail probabilities for Gaussian processes

• 成果类型: Article
• 署名作者: Li, WV; Shao, QM
• 署名单位: University of Delaware; University of Oregon
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 216-242
• 关键词: maximum

摘要

Let X = (X-t)(tis an element ofS) be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P(sup(tis an element ofS)(X-t - X-t0) less than or equal to x) as x --> 0, with t(0) is an element of S fixed. In particular, sharp rates are given for fractional Brownian sheet. Furthermore, connections between lower tail probabilities for Gaussian processes with stationary increments and level crossing probabilities for stationary Gaussian processes are studied. Our methods also provide useful information on a random pursuit problem for fractional Brownian particles.