English

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 X,X, that never hits 0, we construct a pssMp XX^{\downarrow} that hits 0 in a finite time. The latter can be viewed as XX conditioned to hit 0 in a finite time and we prove that this conditioning is determined by the pre-minimum part of X.X. 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}
}