AN EXTENSION OF PITMAN THEOREM FOR SPECTRALLY POSITIVE LEVY PROCESSES

• 成果类型: Article
• 署名作者: BERTOIN, J
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989701
• 发表日期: 1992
• 页码: 1464-1483
• 关键词: excursions; time

摘要

If X is a spectrally positive Levy process, X(c)BAR the continuous part of its maximum process, and J the sum of the jumps of X across its previous maximum, then X - 2X(c)BAR - J has the same law as X conditioned to stay negative. This extends a result due to Pitman, who links the real Brownian motion and the three-dimensional Bessel process. Several other relations between the Brownian motion and the Bessel process are extended in this setting.