A Jump-Type SDE Approach to Real-Valued Self-Similar Markov Processes

Abstract : In his 1972 paper, John Lamperti characterized all positive self-similar Markov processes as time-changes of exponentials of Levy processes. In the past decade the problem of classifying all non-negative self-similar Markov processes that do not necessarily have zero as a trap has been solved gradually via connections to ladder height processes and excursion theory. Motivated by a recent article of Chaumont, Rivero, Panti we classify via jump-type SDEs the symmetric real-valued self-similar Markov processes that only decrease the absolute value by jumps and leave zero continuously. Our construction of these self-similar processes involves a pseudo excursion construction and singular stochastic calculus arguments ensuring that solutions to the SDEs spend zero time at zero to avoid problems caused by a "bang-bang" drift.
Type de document :
Pré-publication, Document de travail
31 pages. 2012
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https://hal.archives-ouvertes.fr/hal-00709194
Contributeur : Leif Doering <>
Soumis le : lundi 18 juin 2012 - 10:38:51
Dernière modification le : lundi 29 mai 2017 - 14:27:10

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  • HAL Id : hal-00709194, version 1
  • ARXIV : 1206.3515

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UPMC | INSMI | PMA | USPC

Citation

Leif Doering. A Jump-Type SDE Approach to Real-Valued Self-Similar Markov Processes. 31 pages. 2012. 〈hal-00709194〉

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