New Methods in Theory and Cosmic Applications of Spherical Random Fields

该项目旨在研究和模拟球形随机场，这些随机场被描述为球体或球上随机微分方程的解。该项目计划研究这些溶液的性质并开发光谱分析。然后计划利用获得的理论结果构建这些随机场的数值逼近和统计估计的新方法。特别是，它计划开发新的渐近和统计方法的张量随机场。该项目将把结果应用于宇宙微波背景数据的建模和分析。预期的结果将提高确定宇宙参数的准确性，并为更好地了解宇宙早期阶段提供新的工具。

This project aims to investigate and model spherical random fields which are described as solutions of stochastic differential equations on a sphere or a ball. The project plans to study properties and develop spectral analysis of these solutions. It then plans to use the obtained theoretical results to construct new methods for numerical approximation and statistical estimation of these random fields. In particular, it plans to develop novel asymptotic and statistical methodology for tensor random fields. The project will apply the results to model and analyse cosmic microwave background data. Expected outcomes will improve the accuracy in determining cosmological parameters and provide novel tools for better understanding of the universe during its early stages.