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July, 1992 An Extension of Pitman's Theorem for Spectrally Positive Levy Processes
Jean Bertoin
Ann. Probab. 20(3): 1464-1483 (July, 1992). DOI: 10.1214/aop/1176989701


If $X$ is a spectrally positive Levy process, $\bar{X}^c$ the continuous part of its maximum process, and $J$ the sum of the jumps of $X$ across its previous maximum, then $X - 2\bar{X}^c - J$ 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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Jean Bertoin. "An Extension of Pitman's Theorem for Spectrally Positive Levy Processes." Ann. Probab. 20 (3) 1464 - 1483, July, 1992.


Published: July, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0760.60068
MathSciNet: MR1175272
Digital Object Identifier: 10.1214/aop/1176989701

Primary: 60J30

Keywords: conditional probability , Levy process , reflected process , spectral positivity

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 3 • July, 1992
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