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

J. Berestycki, L. Döring, L. Mytnik and L. Zambotti

Stochastic Processes and their Applications, 2015, vol. 125, issue 3, 918-940

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 in some cases 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.

Keywords: Continuous state branching processes; Immigration; Self-similarity; Jump-diffusion (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2014.10.012

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