AN EXTENSION OF PITMAN THEOREM FOR SPECTRALLY POSITIVE LEVY PROCESSES

被引：33
|
作者：
BERTOIN, J
机构：
来源：
ANNALS OF PROBABILITY | 1992年 / 20卷 / 03期
关键词：
LEVY PROCESS; SPECTRAL POSITIVITY; REFLECTED PROCESS; CONDITIONAL PROBABILITY;
D O I：
10.1214/aop/1176989701
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：1464 / 1483
页数：20
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