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
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
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