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On some transformations between positive self-similar Markov processes

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  • Chaumont, Loïc
  • Rivero, Víctor

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.

Suggested Citation

  • Chaumont, Loïc & Rivero, Víctor, 2007. "On some transformations between positive self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1889-1909, December.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:12:p:1889-1909
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    References listed on IDEAS

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    1. Chaumont, L., 1996. "Conditionings and path decompositions for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 39-54, November.
    2. Bertoin, J. & Doney, R. A., 1994. "Cramer's estimate for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 363-365, December.
    3. Bertoin, Jean, 1993. "Splitting at the infimum and excursions in half-lines for random walks and Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 17-35, August.
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    Cited by:

    1. Kyprianou, Andreas E. & Vakeroudis, Stavros M., 2018. "Stable windings at the origin," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4309-4325.

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