Report
Fluctuations of stochastic PDEs with long-range correlations
| العنوان: | Fluctuations of stochastic PDEs with long-range correlations |
|---|---|
| المؤلفون: | Gerolla, Luca, Hairer, Martin, Li, Xue-Mei |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematical Physics, 60H15, 60H05, 60F05 |
| الوصف: | We study the large-scale dynamics of the solution to a nonlinear stochastic heat equation (SHE) in dimensions $d \geq 3$ with long-range dependence. This equation is driven by multiplicative Gaussian noise, which is white in time and coloured in space with non-integrable spatial covariance that decays at the rate of $|x|^{-\kappa}$ at infinity, where $\kappa \in (2, d)$. Inspired by recent studies on SHE and KPZ equations driven by noise with compactly supported spatial correlation, we demonstrate that the correlations persist in the large-scale limit. The fluctuations of the diffusively scaled solution converge to the solution of a stochastic heat equation with additive noise whose correlation is the Riesz kernel of degree $-\kappa$. Moreover, the fluctuations converge as a distribution-valued process in the optimal H\"older topologies. Comment: To appear in: the Annals of Applied Probability |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2303.09811 |
| رقم الانضمام: | edsarx.2303.09811 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |