# On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes

Annales de l'I.H.P. Probabilités et statistiques (2013)

- Volume: 49, Issue: 1, page 138-159
- ISSN: 0246-0203

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topFournier, Nicolas. "On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes." Annales de l'I.H.P. Probabilités et statistiques 49.1 (2013): 138-159. <http://eudml.org/doc/272039>.

@article{Fournier2013,

abstract = {We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order $\alpha $ with drift and diffusion coefficients $b$, $\sigma $. When $\alpha \in (1,2)$, we investigate pathwise uniqueness for this equation. When $\alpha \in (0,1)$, we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether $\alpha \in (0,1)$ or $\alpha \in (1,2)$ and on whether the driving stable process is symmetric or not. Our assumptions involve the regularity and monotonicity of $b$ and $\sigma $.},

author = {Fournier, Nicolas},

journal = {Annales de l'I.H.P. Probabilités et statistiques},

keywords = {stable processes; stochastic differential equations with jumps},

language = {eng},

number = {1},

pages = {138-159},

publisher = {Gauthier-Villars},

title = {On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes},

url = {http://eudml.org/doc/272039},

volume = {49},

year = {2013},

}

TY - JOUR

AU - Fournier, Nicolas

TI - On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes

JO - Annales de l'I.H.P. Probabilités et statistiques

PY - 2013

PB - Gauthier-Villars

VL - 49

IS - 1

SP - 138

EP - 159

AB - We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order $\alpha $ with drift and diffusion coefficients $b$, $\sigma $. When $\alpha \in (1,2)$, we investigate pathwise uniqueness for this equation. When $\alpha \in (0,1)$, we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether $\alpha \in (0,1)$ or $\alpha \in (1,2)$ and on whether the driving stable process is symmetric or not. Our assumptions involve the regularity and monotonicity of $b$ and $\sigma $.

LA - eng

KW - stable processes; stochastic differential equations with jumps

UR - http://eudml.org/doc/272039

ER -

## References

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