On some transformations between positive self--similar Markov processes
Probability
2016-08-16 v1
Abstract
A path decomposition at the infimum for positive self-similar Markov processes (pssMp) is obtained. Next, several aspects of the conditioning to hit 0 of a pssMp are studied. Associated to a given a pssMp that never hits 0, we construct a pssMp that hits 0 in a finite time. The latter can be viewed as conditioned to hit 0 in a finite time and we prove that this conditioning is determined by the pre-minimum part of Finally, we provide a method for conditioning a pssMp that hits 0 by a jump to do it continuously.
Keywords
Cite
@article{arxiv.math/0601243,
title = {On some transformations between positive self--similar Markov processes},
author = {Loïc Chaumont and Víctor Manuel Rivero},
journal= {arXiv preprint arXiv:math/0601243},
year = {2016}
}