SUPREMA OF LEVY PROCESSES

• 成果类型: Article
• 署名作者: Kwasnicki, Mateusz; Malecki, Jacek; Ryznar, Michal
• 署名单位: Wroclaw University of Science & Technology; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Universite d'Angers
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP719
• 发表日期: 2013
• 页码: 2047-2065
• 关键词: wiener-hopf factorization; 1st passage; extrema; time

摘要

In this paper we study the supremum functional M-t = sup(0 <= s <= t) X-s, where X-t, t >= 0, is a one-dimensional Levy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative distribution function of Mt. In the symmetric case we find an integral representation of the Laplace transform of the distribution of M-t if the Levy-Khintchin exponent of the process increases on (0, infinity).