论文标题
LDP和CLT用于运输噪声的SPDE
LDP and CLT for SPDEs with Transport Noise
论文作者
论文摘要
在这项工作中，我们考虑了具有传输噪声的随机部分微分方程的解决方案，该方程已知会以适当的缩放限制收敛到具有附加粘度项的相应确定性PDE的溶液。在两种感兴趣的情况下，研究了这种缩放限制的大偏差和高斯波动：尺寸的随机线性传输方程$ d \ geq 2 $和$ 2 $ d $ d euler方程的涡度形式。在这两种情况下，都建立了具有强收敛和明确速率的中央限制定理。这些证明依赖于非平凡的工具，例如具有超临界系数的传输方程和$γ$ - convergence的参数。
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large deviations and Gaussian fluctuations underlying such scaling limit are investigated in two cases of interest: stochastic linear transport equations in dimension $D\geq 2$ and $2$D Euler equations in vorticity form. In both cases, a central limit theorem with strong convergence and explicit rate is established. The proofs rely on nontrivial tools, like the solvability of transport equations with supercritical coefficients and $Γ$-convergence arguments.
