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

J. Berestycki; L. Döring; Leonid Mytnik; L. Zambotti

doi:10.1016/j.spa.2014.10.012

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

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

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	918-940
Number of pages	23
Journal	Stochastic Processes and their Applications
Volume	125
Issue number	3
DOIs	https://doi.org/10.1016/j.spa.2014.10.012
State	Published - Mar 2015

Keywords

Continuous state branching processes
Immigration
Jump-diffusion
Self-similarity

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/j.spa.2014.10.012

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AU - Mytnik, Leonid

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AB - 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.

KW - Continuous state branching processes

KW - Immigration

KW - Jump-diffusion

KW - Self-similarity

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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