Academic Journal
Weak existence for SDEs with singular drifts and fractional Brownian or Levy noise beyond the subcritical regime ...
| Title: | Weak existence for SDEs with singular drifts and fractional Brownian or Levy noise beyond the subcritical regime ... |
|---|---|
| Authors: | Butkovsky, Oleg, Gallay, Samuel |
| Publisher Information: | arXiv |
| Publication Year: | 2023 |
| Collection: | DataCite Metadata Store (German National Library of Science and Technology) |
| Subject Terms: | Probability math.PR, FOS Mathematics |
| Description: | We study a multidimensional stochastic differential equation with additive noise: $$ d X_t=b(t, X_t) dt +d ξ_t, $$ where the drift $b$ is integrable in space and time, and $ξ$ is either a fractional Brownian motion or an $α$-stable process. We show weak existence of solutions to this equation under the optimal condition on integrability indices of $b$, going beyond the subcritical Krylov-Röckner (Prodi-Serrin-Ladyzhenskaya) regime. This extends the recent results of Krylov (2020) to the fractional Brownian and Lévy cases. We also construct a counterexample to demonstrate the optimality of this condition. Our methods are built upon a version of the stochastic sewing lemma of Lê and the John--Nirenberg inequality. ... |
| Document Type: | article in journal/newspaper report |
| Language: | unknown |
| DOI: | 10.48550/arxiv.2311.12013 |
| Availability: | https://doi.org/10.48550/arxiv.2311.12013 https://arxiv.org/abs/2311.12013 |
| Rights: | Creative Commons Attribution 4.0 International ; https://creativecommons.org/licenses/by/4.0/legalcode ; cc-by-4.0 |
| Accession Number: | edsbas.380423EC |
| Database: | BASE |
| Description not available. |