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

Technion - Israel Institute of Technology

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

All Science Journal Classification (ASJC) codes

Applied Mathematics
Statistics and Probability
Modelling and Simulation

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10.1016/j.spa.2014.10.012

Cite this

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abstract = "We study a class of self-similar jump type SDEs driven by H{\"o}lder 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.",

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author = "J. Berestycki and L. D{\"o}ring and Leonid Mytnik and L. Zambotti",

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T1 - Hitting properties and non-uniqueness for SDEs driven by stable processes

AU - Berestycki, J.

AU - Döring, L.

AU - Mytnik, Leonid

AU - Zambotti, L.

PY - 2015/3

Y1 - 2015/3

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84919667058&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2014.10.012

DO - 10.1016/j.spa.2014.10.012

M3 - مقالة

SN - 0304-4149

VL - 125

SP - 918

EP - 940

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 3

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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