Hitting properties and non-uniqueness for SDE driven by stable processes

Abstract : We study a class of self-similar jump type SDEs driven by Hölder-continuous drift and noise coefficients. Using the Lamperti transformation for positive self-similar Markov processes we obtain a necessary and sufficient condition for almost sure extinction in finite time. We then show that for certain parameters pathwise uniqueness holds in a restricted sense, namely among solutions spending a Lebesgue-negligible amount of time at 0. A direct power transformation plays a key role.
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Preprints, Working Papers, ...
2011
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https://hal.archives-ouvertes.fr/hal-00706796
Contributor : Lorenzo Zambotti <>
Submitted on : Monday, June 11, 2012 - 3:41:07 PM
Last modification on : Monday, May 29, 2017 - 2:26:42 PM

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  • HAL Id : hal-00706796, version 1
  • ARXIV : 1111.4388

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Citation

Julien Berestycki, Leif Doering, Leonid Mytnik, Lorenzo Zambotti. Hitting properties and non-uniqueness for SDE driven by stable processes. 2011. 〈hal-00706796〉

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