Set-indexed and multiparameter stochastic processes

集合索引和多参数随机过程

• 批准号: 3459-2007
• 负责人: Ivanoff, Gail
• 金额: $ 2.11万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=364039
• 关键词: Set; indexed; multiparameter; stochastic; processes

Random processes indexed by a multidimensional time parameter, or more generally, by a class of sets, may be used to model many stochastic phenomena and have been the focus of much research activity in recent years. However, the passage from a totally ordered index set (time) to a partially ordered one (multidimensional time or sets) introduces many challenges. In particular, describing the dynamical properties of the process (i.e. how the process evolves)becomes far more complicated. Elegant tools such as martingale and Markov process theory need to be extended to this more general framework.In this research, we will be considering the analysis of set-indexed processes that are only partially observable; that is, the process may be obscured on some (random) set. In this case, we say that the process is filtered by the set. We will investigate survival analysis of filtered data and as well precedence-type tests. We will also consider the converse situation, in which the set-indexed process can be totally observed, but its behaviour changes on a random set that cannot be observed. In this case, we want to find an optimum manner of detecting the set.All of these techniques will lead to new methods of analyzing geographic and biomedical data sets in which each data point is multidimensional.

由多维时间参数索引的随机过程，或更普遍地通过一类集合来模拟许多随机现象，并且近年来一直是许多研究活动的重点。但是，从完全有序的索引集（时间）到部分订购的一个（多维时间或集合）的段落引入了许多挑战。特别是，描述过程的动力学特性（即过程如何发展）变得更加复杂。诸如Martingale和Markov流程理论之类的优雅工具需要扩展到这个更一般的框架。在这项研究中，我们将考虑对仅部分可观察到的设置索引过程的分析；也就是说，该过程可能会在某些（随机）集中遮盖。在这种情况下，我们说该过程被集合过滤。我们将研究过滤数据的生存分析以及优先型型测试。我们还将考虑可以完全观察到的设置索引过程的相反情况，但其行为在无法观察到的随机集合上发生了变化。在这种情况下，我们希望找到一种最佳的检测方式。这些技术的所有内容都将导致分析每个数据点具有多维的地理和生物医学数据集的新方法。