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，强大而新颖的正则结构和副控制分布理论主要用于推导奇异随机偏微分方程（SPDE）的存在性、唯一性和正则性结果。我们认为，现在进一步探索这些技术的全部威力的时机已经成熟：将它们扩展为导出解决方案的定性属性，特别是诸如老化和间歇性等物理效应。我们将对两个最突出和最有前途的方程（Kardar-Parisi-Zhang 方程和抛物线 Anderson 模型）执行此操作。通过结合我们在老化和间歇性（J.-D.D. 和 W.K.）以及副控制分布/正则结构（N.P.）方面的专业知识，我们掌握了广泛的技术，这将使我们能够更好地理解这些方程。