Pré-Publication, Document De Travail Année : 2006

On some transformations between positive self--similar Markov processes

Résumé

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

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Dates et versions

hal-00016781 , version 1 (11-01-2006)

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Loïc Chaumont, Víctor Manuel Rivero. On some transformations between positive self--similar Markov processes. 2006. ⟨hal-00016781⟩
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