High-dimensional statistics for point and jump processes

点和跳跃过程的高维统计

• 批准号: 439154027
• 负责人: Professor Dr. Mathias Trabs
• 金额: --
• 依托单位: Forschungsgebiet Mathematische Informatik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/439154027?language=en
• 关键词: dimensional; statistics; point; jump; processes

Whenever the evolution of a time dependent system is influenced by random phenomena, stochastic processes are used for mathematical modelling. The applications are manifold appearing in natural sciences as well as in engineering, econometrics and financial mathematics. The calibration of these probabilistic models is a fundamental requirement for their application and has attracted much attention in the last decades. While, except for a few examples, most of the statistical research for stochastic processes is restricted to one-dimensional or low-dimensional models, an important feature of data sets in modern applications is high dimensionality, i.e., the dimension of the parameter space or dimension of the process may increase with the sample size. Examples include a huge number of covariates which potentially influence the evolution of biochemical processes as well as large portfolios in financial markets. It is well known that classical procedures fail if the dimension is large and various novel methods of high-dimensional parameter estimation have been developed. The aim of this project is to combine the statistical theory for stochastic processes with high-dimensional statistics to construct and analyse new statistical methods for high-dimensional stochastic processes.

每当时间相关系统的演化受到随机现象的影响时，随机过程就用于数学建模。这些应用广泛出现在自然科学以及工程、计量经济学和金融数学中。这些概率模型的校准是其应用的基本要求，并且在过去几十年中引起了广泛关注。虽然除了少数例子外，大多数随机过程的统计研究仅限于一维或低维模型，但现代应用中数据集的一个重要特征是高维性，即参数空间或参数空间的维数。过程的维度可能会随着样本大小的增加而增加。例子包括大量可能影响生化过程演变的协变量以及金融市场中的大型投资组合。众所周知，如果维数很大，经典程序就会失败，并且已经开发了各种高维参数估计的新方法。该项目的目的是将随机过程的统计理论与高维统计相结合，构建和分析高维随机过程的新统计方法。