Inverting the Signature Transform for Rough Paths and Random Processes

签名变换提供了在高度振荡且涉及复杂随机性的多维路径中编码的基本信息的有效总结。这个项目的主要目标是开发新的算法方法，从签名变换中重建不同量化水平的粗糙路径和随机过程。本项目期望在签名求逆这一重大公开问题上取得理论突破，从而促进粗糙路径理论和随机分析领域的知识进步。新开发的方法将与新兴的基于签名的方法相结合，用于研究金融数据分析和视觉语音识别中的重要问题。

The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significant open problem of signature inversion, thereby advancing knowledge in the areas of rough path theory and stochastic analysis. The newly developed methods will be utilised in combination with the emerging signature-based approach to study important problems in financial data analysis and visual speech recognition.