Persistence of integrated stable processes

• 成果类型: Article
• 署名作者: Profeta, Christophe; Simon, Thomas
• 署名单位: Universite Paris Saclay; Universite de Lille; Universite Paris Saclay
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0577-5
• 发表日期: 2015
• 页码: 463-485
• 关键词: brownian-motion; sums; asymptotics

摘要

We compute the persistence exponent of the integral of a stable L,vy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Shi (Lower tails of some integrated processes. In: Small deviations and related topics (problem panel 2003). Along the way, we investigate the law of the stable process evaluated at the first time its integral hits zero, when the bivariate process starts from a coordinate axis. This extends classical formul' by McKean (J Math Kyoto Univ 2:227-235, 1963) and Gor'kov (Soviet. Math. Dokl. 16:904-908, 1975) for integrated Brownian motion.