Mathematical Sciences: Brownian Motion and Related Stochastic Processes

数学科学：布朗运动和相关随机过程

• 批准号: 9107531
• 负责人: James Pitman
• 金额: $ 12.14万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1994-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107531&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Brownian; Motion; Related

The principal investigator, together with his collaborator Marc Yor, will continue his present lines of research into stochastic processes, particularly Brownian motion and related processes. Attention will be focussed on problems amenable to treatment using the tools of martingale calculus, local time and excursion theory. Particular subjects for study are the following: interval partitions associated with a subordinator, multiple points of Brownian motion in dimensions 2 and 3, Tsirelson's equations in discrete time, non-canonical decompositions of Brownian motion, the Ciesielski-Taylor identities in law, multivariate Cauchy variables and affine decompositions of a stable variable of index (1/2), intertwinings of Markov processes, and characterization of the Brownian filtration. The principal investigator, together with his collaborator Marc Yor, will continue his present lines of research into stochastic processes, particularly Brownian motion and related processes. Attention will be focussed on problems amenable to treatment using the tools of martingale calculus, local time and excursion theory. Stochastic processes represent an important area of research in probability theory.

首席研究员和他的合作者Marc Yor将继续他目前对随机过程，特别是布朗运动和相关过程的研究。关注的问题将集中在适合于处理的问题上，利用鞅演算、当地时间和游程理论的工具。具体的研究主题如下：与从属有关的区间划分，2维和3维的多个布朗运动点，离散时间中的齐勒森方程，布朗运动的非正则分解，定律中的Ciesielski-Taylor恒等式，多元柯西变量和指数(1/2)稳定变量的仿射分解，马尔可夫过程的交织，以及布朗滤子的特征。首席研究员和他的合作者Marc Yor将继续他目前对随机过程，特别是布朗运动和相关过程的研究。关注的问题将集中在适合于处理的问题上，利用鞅演算、当地时间和游程理论的工具。随机过程是概率论研究的一个重要领域。