On some transformations between positive self-similar Markov processes |
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| Authors: | Loïc Chaumont Víctor Rivero |
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| Institution: | 1. Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, 4, Place Jussieu - 75252 Paris Cedex 05, France;2. CIMAT A.C. Calle Jalisco s/n, C.P. 36240, Guanajuato, Gto., Mexico;3. Université Paris X, Nanterre, MODAL’X, 200, Avenue de la République, 92001, Nanterre Cedex, France |
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| 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 pssMp X, that never hits 0, we construct a pssMp X↓ 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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| Keywords: | 60G18 60G17 |
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