Mathematical Sciences: Research in Stochastic Processes

数学科学：随机过程研究

• 批准号: 8802288
• 负责人: Jay Rosen
• 金额: $ 8.44万
• 依托单位: CUNY College of Staten Island
• 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: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802288&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Stochastic; Processes

The three general areas of research are Brownian motion on manifolds, measure valued processes, and the range of a random walk. The unifying theme among them is the study of intersection local times. The research is generalization to manifolds of the results previously obtained by the investigator. Various forms of intersection local times are used. Study of the local times for Levy processes is prompted due to the relatively recent discovery of the necessary and sufficient condition for sample continuity of a stationary Gaussian process. The isolation of the regular part of the intersection local times of higher orders lead in a normal way to the study of anticipative integrands. Various new methods developed for these integrands will contribute towards the study of the higher order intersection local times.

三个一般的研究领域是布朗运动， 流形、测度值过程和随机数的值域 步行. 它们之间的统一主题是交叉研究 当地时间。 本文的研究推广到了 研究者先前获得的结果。 各种形式 使用交叉口的当地时间。 地方时报研究 对于Levy过程，由于相对较新的 发现样本的充分必要条件 平稳高斯过程的连续性。 分离 高阶局部时交的正则部分 以一种正常的方式引导对预期被积函数的研究。 为这些被积体开发的各种新方法将 有助于高阶交的研究 当地时间。