A diagram-free approach to the stochastic estimates in regularity structures
A diagram-free approach to the stochastic estimates in regularity structures
复制标题
正则结构中随机估计的无图方法
DOI：
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复制
发表时间：
2021
影响因子：
3.1
通讯作者：
P. Tsatsoulis
中科院分区：
文献类型：
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作者：
P. Linares;F. Otto;Markus Tempelmayr;P. Tsatsoulis
在本文中，我们探索了基于比树更贪婪的索引集的Hairer正则性结构的版本，如在（Otto等人，在完全亚临界状态下准线性SPDE的先验界限，2021，arXiv：2103.11039）中引入的，并且在（Linares等人，在Comm. Am. Math.Soc.3：1-64，2023）。更准确地说，我们构建和随机估计中假设的重整化模型（Otto et al. in A priori bounds for quasi-linear SPDE in the full sub-critical regime，2021，arXiv：2103.11039），避免使用费曼图，但仍然是以全自动的方式，即归纳的方式。这是进行了一类拟线性抛物型偏微分方程驱动的噪声在全奇异，但renormalizable范围。我们假设一个频谱间隙不等式（不一定是高斯）噪声合奏。由此产生的控制模型的方差自然补充其消失的期望所产生的BPHZ选择的重整化。我们捕获的增益的规律性的Malliavin衍生物的模型，通过将其描述为一个模拟的分布。对称性是一个重要的指导原则，并内置在重整化Ancel的水平。我们的方法是分析和自上而下，而不是组合和自下而上。
In this paper, we explore the version of Hairer’s regularity structures based on a greedier index set than trees, as introduced in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-critical regime, 2021, arXiv:2103.11039) and algebraically characterized in (Linares et al. in Comm. Am. Math. Soc. 3:1–64, 2023). More precisely, we construct and stochastically estimate the renormalized model postulated in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-critical regime, 2021, arXiv:2103.11039), avoiding the use of Feynman diagrams but still in a fully automated, i. e. inductive way. This is carried out for a class of quasi-linear parabolic PDEs driven by noise in the full singular but renormalizable range. We assume a spectral gap inequality on the (not necessarily Gaussian) noise ensemble. The resulting control on the variance of the model naturally complements its vanishing expectation arising from the BPHZ-choice of renormalization. We capture the gain in regularity on the level of the Malliavin derivative of the model by describing it as a modelled distribution. Symmetry is an important guiding principle and built-in on the level of the renormalization Ansatz. Our approach is analytic and top-down rather than combinatorial and bottom-up.
基于谱间隙不等式的正则结构的 BPHZ 定理
DOI：
10.48550/arxiv.2301.10081
发表时间：
2023
期刊：
arXiv e-prints
影响因子：
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作者：
Hairer Martin
通讯作者：
Hairer Martin