Inverting the Signature Transform for Rough Paths and Random Processes

粗糙路径和随机过程的逆签名变换

• 批准号: DE210101352
• 负责人: Dr Xi Geng
• 金额: $ 23.2万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-07-12 至 2024-07-11
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE210101352
• 关键词: Inverting; Signature; Transform; Rough; Paths

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.

签名变换提供了编码在多维路径中的基本信息的有效总结，这些多维路径是高度振荡的并且涉及复杂的随机性。该项目的主要目标是开发新的算法方法，以从各种定量水平的签名变换中重建粗糙路径和随机过程。本项目期望在特征反演这一重要的开放性问题上取得理论突破，从而推进粗糙路径理论和随机分析领域的知识。新开发的方法将结合新兴的基于签名的方法来研究金融数据分析和视觉语音识别中的重要问题。