An Extension of Pitman's Theorem for Spectrally Positive Levy Processes
Bertoin, Jean
Ann. Probab., Tome 20 (1992) no. 4, p. 1464-1483 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1992-07-14
Classification:  Levy process,  spectral positivity,  reflected process,  conditional probability,  60J30 
@article{1176989701,
     author = {Bertoin, Jean},
     title = {An Extension of Pitman's Theorem for Spectrally Positive Levy Processes},
     journal = {Ann. Probab.},
     volume = {20},
     number = {4},
     year = {1992},
     pages = { 1464-1483},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989701}
}

Bertoin, Jean. An Extension of Pitman's Theorem for Spectrally Positive Levy Processes. Ann. Probab., Tome 20 (1992) no. 4, pp.  1464-1483. http://gdmltest.u-ga.fr/item/1176989701/