Change-Point Detection for Discretely Sampled Diffusion Processes

离散采样扩散过程的变化点检测

• 批准号: 208420571
• 负责人: Dr. Stefan-Radu Mihalache
• 金额: --
• 依托单位: Abteilung Mathematik
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2011-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/208420571?language=en
• 关键词: Change; Point; Detection; Discretely; Sampled

While in the case of discrete-time series of random variables, e.g. regression models, a lot of statistical procedures for all kinds of problems of a model change (change-point problem) already exist, it has been payed little attention to the statistical detection of such change-points in (continuous-time, non-deterministic) solutions of stochastic differential equations (diffusions) yet. Typically, a change-point denotes the time point in the observation period where the parameters determining the model change. Aim of this project is to provide a contribution to bridging the gap between discrete-time and continuous-time approaches for detecting change-points in statistical models. Toward this end, it is intended to extend the developed statistical test procedures of the own Ph.D. thesis to settings of the problem suitable for applications. E.g., stochastic differential equations represent a modern tool for mathematical modelling of financial data or of physiological processes such as the dynamics of the glucose-insulin balance and neuronal processes. Primarily at physiological models, one can benefit from the considerable experience in Copenhagen in order to adapt the mathematical assumptions to the requirements in fields of application. The focus is on obtaining the necessary information about the continuous-time evolution of the diffusion from discrete, i.e. finitely many, data. Moreover, the following generalisations of the model are planned: multidimensional parametric diffusions with also multidimensional parameters and diffusions which only exist in subsets of the whole space. In the context of this project, the intended results are several powerful test procedures including a monitoring procedure (sequential test) allowing an evaluation of the parameters already during the observation period.

而对于随机变量的离散时间序列，如回归模型，对于模型变化的各种问题（变点问题）已经有了大量的统计方法，但对于随机微分方程（扩散）的（连续时间、非确定性）解中这种变点的统计检测却很少有人关注。通常，变化点表示观测周期中决定模型的参数发生变化的时间点。这个项目的目的是提供一个贡献，以弥合离散时间和连续时间方法之间的差距，以检测统计模型中的变化点。为了达到这个目的，它的目的是扩展自己的博士论文的开发统计测试程序的设置适合应用的问题。例如，随机微分方程代表了金融数据或生理过程（如葡萄糖-胰岛素平衡和神经元过程的动力学）数学建模的现代工具。主要在生理模型方面，人们可以从哥本哈根的大量经验中受益，以便使数学假设适应应用领域的要求。重点是从离散的，即有限多的数据中获得关于扩散的连续时间演化的必要信息。此外，规划了模型的以下推广：具有多维参数的多维参数扩散和仅存在于整个空间子集中的扩散。在这个项目的背景下，预期的结果是几个强大的测试程序，包括一个监测程序（顺序测试），允许在观察期间对参数进行评估。