Athreya, Siva ; Butkovsky, Oleg ; Mytnik, Leonid (2020) Strong existence and uniqueness for stable stochastic differential equations with distributional drift The Annals of Probability, 48 (1). ISSN 0091-1798
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Official URL: http://doi.org/10.1214/19-AOP1358
Related URL: http://dx.doi.org/10.1214/19-AOP1358
Abstract
We consider the stochastic differential equation dXt=b(Xt)dt+dLt, where the drift b is a generalized function and L is a symmetric one dimensional α-stable Lévy processes, α∈(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 Cβ for β<1/2−α/2.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Institute of Mathematical Statistics |
| Keywords: | Regularization by noise , Stable processes , Stochastic differential equations , Strong solution , Zvonkin transformation |
| ID Code: | 131655 |
| Deposited On: | 07 Dec 2022 10:44 |
| Last Modified: | 07 Dec 2022 10:44 |
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