1
|
Galeati L, Ling C. Stability estimates for singular SDEs and applications. ELECTRON J PROBAB 2023. [DOI: 10.1214/23-ejp913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Affiliation(s)
- Lucio Galeati
- École Polytechnique Fédérale de Lausanne, Bâtiment MA, 1015 Lausanne, Switzerland
| | - Chengcheng Ling
- Technische Universität Wien, Institute of Analysis and Scientific Computing, 1040 Wien, Austria
| |
Collapse
|
2
|
Distribution dependent SDEs driven by additive fractional Brownian motion. Probab Theory Relat Fields 2022. [DOI: 10.1007/s00440-022-01145-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
AbstractWe study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $$H\in (0,1)$$
H
∈
(
0
,
1
)
. We establish strong well-posedness under a variety of assumptions on the drift; these include the choice $$\begin{aligned} B(\cdot ,\mu )=(f*\mu )(\cdot ) + g(\cdot ), \quad f,\,g\in B^\alpha _{\infty ,\infty },\quad \alpha >1-\frac{1}{2H}, \end{aligned}$$
B
(
·
,
μ
)
=
(
f
∗
μ
)
(
·
)
+
g
(
·
)
,
f
,
g
∈
B
∞
,
∞
α
,
α
>
1
-
1
2
H
,
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.
Collapse
|