On some transformations between positive self-similar Markov processes
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[downwards arrow] 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.
Year of publication: |
2007
|
---|---|
Authors: | Chaumont, Loïc ; Rivero, Víctor |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 117.2007, 12, p. 1889-1909
|
Publisher: |
Elsevier |
Keywords: | Self-similar Markov processes Lévy processes Weak convergence Decomposition at the minimum Conditioning h-transforms |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Quasi-stationary distributions and Yaglom limits of self-similar Markov processes
Haas, Bénédicte, (2012)
- More ...