Mathematical Sciences: Studies on Markov Chains and Branching Processes

数学科学：马尔可夫链和分支过程的研究

• 批准号: 9204938
• 负责人: Krishna Athreya
• 金额: $ 6万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204938&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Markov; Chains

Research will continue in the areas of nonlinear filtering, Markov chains, and branching processes. In nonlinear filtering, approximations will be studied and comparisons will be made between various approximations. For Markov chains on a general state space, consistent and asymptotically normal estimates of the transition function are to be sought. Large deviations of the estimates of the population in a supercritical branching process will also be investigated. Research will be done on distinguishing between the original signal and interference when a signal has been received. In addition, attempts will be made to estimate the probability structure of certain types of randomly evolving processes.

研究将继续在非线性过滤，马尔可夫链和分支过程的领域继续进行。 在非线性过滤中，将研究近似值，并将在各种近似值之间进行比较。 对于马尔可夫链上的一般状态空间，要寻求一致和渐近的正常估计值。 还将研究在超临界分支过程中人口估计值的巨大偏差。 将在接收信号时区分原始信号和干扰的研究。 另外，将尝试估计某些类型的随机发展过程的概率结构。