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.

在非线性滤波、马尔可夫链和分支过程等领域的研究将继续进行。在非线性滤波中，我们将研究各种近似，并对各种近似进行比较。对于一般状态空间上的马尔可夫链，寻求转移函数的一致渐近正态估计。在超临界分支过程中种群估计的大偏差也将被研究。当接收到信号时，将研究如何区分原始信号和干扰。此外，将尝试估计某些类型的随机演化过程的概率结构。