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Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2013

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

Résumé

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 $\sigma$.

Dates et versions

hal-00731705 , version 1 (13-09-2012)

Identifiants

Citer

Nicolas Fournier. On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2013, 49 (1), pp.138-159. ⟨10.1214/11-AIHP420⟩. ⟨hal-00731705⟩
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