Mathematical Sciences: Markov Processes and Related Topics

数学科学：马尔可夫过程及相关主题

• 批准号: 8721347
• 负责人: Michael Sharpe
• 金额: $ 27.37万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-05-15 至 1991-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8721347&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Markov; Processes; Related

This group of outstanding researcher propose to continue their studies in to probabilistic potential theory. A new definition of capacity and co-capacity based on Kuznetsov measures is used. Since this does not use the assumption of duality, a general framework for potential theory is expected to emerge. Specific problems to be worked on include transformations of Kuznetsov processes that preserve the Markov property, relationships of homogeneous random measures and entrance laws, existence of right processes with given hitting distributions and general theory of h-transforms of bi-Brownian motions.

这群杰出的研究人员建议继续他们对概率势理论的研究。使用了基于库兹涅佐夫度量的容量和共容量的新定义。由于这不使用二元性假设，势能理论的一般框架有望出现。需要研究的具体问题包括保持马氏性的Kuznetsov过程的变换，齐次随机测度与入口律的关系，给定命中分布的右过程的存在性，以及双布朗运动的h变换的一般理论。