Abstract
We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter H∈ (0 , 1). We establish strong well-posedness under a variety of assumptions on the drift; these include the choice B(·,μ)=(f∗μ)(·)+g(·),f,g∈B∞,∞α,α>1-12H,thus extending the results by Catellier and Gubinelli (Stochast Process Appl 126(8):2323–2366, 2016) to the distribution dependent case. The proofs rely on some novel stability estimates for singular SDEs driven by fractional Brownian motion and the use of Wasserstein distances.
| Original language | English |
|---|---|
| Pages (from-to) | 251-309 |
| Number of pages | 59 |
| Journal | Probability Theory and Related Fields |
| Volume | 185 |
| Issue number | 1-2 |
| Early online date | 20 May 2022 |
| DOIs | |
| Publication status | Published - 1 Feb 2023 |
Bibliographical note
Funding Information:FH gratefully acknowledges financial support from the STORM Project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany’s Excellence Strategy - GZ 2047/1, Project-id 390685813.
Funding
FH gratefully acknowledges financial support from the STORM Project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany’s Excellence Strategy - GZ 2047/1, Project-id 390685813.
Keywords
- Distribution dependent SDEs
- Fractional Brownian motion
- Regularization by noise
- Singular drifts
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty