Mathematical Sciences: Non-adapted Stochastic Differential Systems

数学科学：非适应随机微分系统

• 批准号: 8903014
• 负责人: Daniel Ocone
• 金额: $ 4.18万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903014&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Non; adapted; Stochastic

The principal investigator will study non-adaptive differential systems. Non-adaptive differential systems are stochastic (random) differential equations whose solutions are not adapted to the driving noise, either because the coefficients of the equation anticipate the noise or because boundary conditions are imposed at the final time. The investigator will continue to study such systems by using a new stochastic calculus developed by Nualart and Pardoux for stochastic integral with anticipating integrands. One aspect of the research involves collaboration with E. Pardoux. They will investigate Markov field properties and filtering for stochastic bilinear equations with boundary conditions.

首席研究员将研究非自适应微分系统。非自适应微分系统是随机（随机）微分方程，其解不适应驱动噪声，要么是因为方程的系数预测了噪声，要么是因为在最后时刻施加了边界条件。研究者将继续使用Nualart和Pardoux开发的具有预期积分的随机积分的新随机微积分来研究这样的系统。这项研究的一个方面涉及与E. Pardoux的合作。他们将研究具有边界条件的随机双线性方程的马尔可夫场性质和滤波。