On some transformations between positive self-similar Markov processes

Loïc Chaumont and Víctor Rivero

Stochastic Processes and their Applications, 2007, vol. 117, issue 12, 1889-1909

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[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.

Keywords: Self-similar; Markov; processes; Lévy; processes; Weak; convergence; Decomposition; at; the; minimum; Conditioning; h-transforms (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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