## The Annals of Probability

### An Extension of Pitman's Theorem for Spectrally Positive Levy Processes

Jean Bertoin

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 20, Number 3 (1992), 1464-1483.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989701

Digital Object Identifier
doi:10.1214/aop/1176989701

Mathematical Reviews number (MathSciNet)
MR1175272

Zentralblatt MATH identifier
0760.60068

JSTOR