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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=520586
• 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.

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。