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January 2020 Strong existence and uniqueness for stable stochastic differential equations with distributional drift
Siva Athreya, Oleg Butkovsky, Leonid Mytnik
Ann. Probab. 48(1): 178-210 (January 2020). DOI: 10.1214/19-AOP1358

Abstract

We consider the stochastic differential equation \begin{equation*}dX_{t}=b(X_{t})\,dt+dL_{t},\end{equation*} where the drift $b$ is a generalized function and $L$ is a symmetric one dimensional $\alpha $-stable Lévy processes, $\alpha \in (1,2)$. We define the notion of solution to this equation and establish strong existence and uniqueness whenever $b$ belongs to the Besov–Hölder space $\mathcal{C}^{\beta }$ for $\beta >1/2-\alpha /2$.

Citation

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Siva Athreya. Oleg Butkovsky. Leonid Mytnik. "Strong existence and uniqueness for stable stochastic differential equations with distributional drift." Ann. Probab. 48 (1) 178 - 210, January 2020. https://doi.org/10.1214/19-AOP1358

Information

Received: 1 January 2018; Revised: 1 November 2018; Published: January 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07206756
MathSciNet: MR4079434
Digital Object Identifier: 10.1214/19-AOP1358

Subjects:
Primary: 60G52, 60H10

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • January 2020
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