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Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift
- Publication Year :
- 2024
-
Abstract
- We are interested in the discretization of stable driven SDEs with additive noise for $\alpha$ $\in$ (1, 2) and Lq -- Lp drift under the Serrin type condition $\alpha$/q + d/p < $\alpha$ -- 1. We show weak existence and uniqueness as well as heat kernel estimates for the SDE and obtain a convergence rate of order (1/$\alpha$)*($\alpha$ -- 1 -- $\alpha$/q - d/p) for the difference of the densities for the Euler scheme approximation involving suitably cutoffed and time randomized drifts.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.08378
- Document Type :
- Working Paper