Well-posedness and Hurst parameter estimation for fluid equations driven by fractional transport noise
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913011672809472 |
|---|---|
| author | Neamtu, Alexandra Blessing Crisan, Dan Lang, Oana |
| author_facet | Neamtu, Alexandra Blessing Crisan, Dan Lang, Oana |
| contents | We study a two-dimensional incompressible vorticity equation on the torus driven by transport-type fractional Brownian noise with Hurst parameter $H \in (1/2,1)$. The model captures persistent, long-range correlated forcing consistent with inertial-range scaling laws and fractional Brownian approximations of turbulent fluctuations. A central ingredient of our approach is a version of the sewing lemma adapted to a class of integrands that includes, but is not limited to, transport-type structures. This result provides a flexible tool for constructing the Young integral and serves as a basis for analysing a wider class of stochastic partial differential equations. Using this approach, we establish existence and uniqueness of solutions via a fixed point argument and investigate statistical properties of the flow. In particular, we study quadratic functionals of the solution and derive an estimator for the Hurst parameter $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05910 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness and Hurst parameter estimation for fluid equations driven by fractional transport noise Neamtu, Alexandra Blessing Crisan, Dan Lang, Oana Probability Mathematical Physics Analysis of PDEs Functional Analysis Statistics Theory We study a two-dimensional incompressible vorticity equation on the torus driven by transport-type fractional Brownian noise with Hurst parameter $H \in (1/2,1)$. The model captures persistent, long-range correlated forcing consistent with inertial-range scaling laws and fractional Brownian approximations of turbulent fluctuations. A central ingredient of our approach is a version of the sewing lemma adapted to a class of integrands that includes, but is not limited to, transport-type structures. This result provides a flexible tool for constructing the Young integral and serves as a basis for analysing a wider class of stochastic partial differential equations. Using this approach, we establish existence and uniqueness of solutions via a fixed point argument and investigate statistical properties of the flow. In particular, we study quadratic functionals of the solution and derive an estimator for the Hurst parameter $H$. |
| title | Well-posedness and Hurst parameter estimation for fluid equations driven by fractional transport noise |
| topic | Probability Mathematical Physics Analysis of PDEs Functional Analysis Statistics Theory |
| url | https://arxiv.org/abs/2604.05910 |