Singular SPDEs: Approximation and Statistical Properties

奇异 SPDE：近似和统计特性

• 批准号: 288774288
• 负责人: Professor Dr. Wolfgang König
• 金额: --
• 依托单位: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/288774288?language=en
• 关键词: Singular; SPDEs; Approximation; Statistical; Properties

The powerful and novel theories of regularity structures and paracontrolled distributions have so far been used mostly for deriving existence, uniqueness and regularity results for singular stochastic partial differential equations (SPDEs). We feel that the time is now mature for a further exploration of the full power of these techniques: to extend them for deriving qualitative properties of the solutions, in particular physical effects such as aging and intermittency and alike. We will do this for two of the most prominent and promising equations, the Kardar-Parisi-Zhang equation and the parabolic Anderson model. By combining our expertise in aging and intermittency (J.-D.D. and W.K.) and paracontrolled distributions / regularity structures (N.P.) respectively, we dispose of a wide range of techniques which will allow us to gain a much better understanding of these equations.

迄今为止，有力的规律结构和副控制分布的强大而新颖的理论主要用于得出存在的存在，独特性和规律性结果的奇异随机偏微分方程（SPDE）。我们认为，现在的时间已经成熟，以进一步探索这些技术的全部力量：将它们扩展为推导解决方案的定性特性，特别是物理效应，例如衰老，间歇性和相似之处。我们将为两个最突出，最有前途的方程式，Kardar-Parisi-Zhang方程和抛物线代理Anderson模型来执行此操作。通过将我们在老化和间歇性方面的专业知识（J.-D.D.和W.K.）和paracontroll的分布 /规则性结构（N.P.）结合在一起，我们处置了广泛的技术，这将使我们能够更好地了解这些方程。