Article ID Journal Published Year Pages File Type
1157031 Stochastic Processes and their Applications 2007 21 Pages PDF
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 XX, that never hits 0, we construct a pssMp X↓X↓ 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 XX. Finally, we provide a method for conditioning a pssMp that hits 0 by a jump to do it continuously.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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