Mathematical Sciences: Limit Theory and Large Deviation Theory of Markov and Infinite Memory Chains with Applications to Physical Models

数学科学：马尔可夫和无限记忆链的极限理论和大偏差理论及其在物理模型中的应用

• 批准号: 9625552
• 负责人: Peter Ney
• 金额: $ 6万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625552&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Limit; Theory; Large

9625552 Ney ABSTRACT Research will be carried out in two general areas: large deviation theory, and cascade theory. In large deviation theory, regeneration and renewal methods will be used to extend the applicability of sub-additivity arguments to Markov additive processes and to infinite memory chains. This yields quick and direct methods to establish existence of a large deviation principle. New techniques for identifying the relevant rate functions will be investigated. Large deviation of the iterates of certain monotone maps related to the infinite order chains will be studies by the above methods. Electron-photon cascades will be studied as special cases of multi-type branching random walks. An open question on the balance between electrons and photons above a fixed energy at large depths of an absorber will be studied. Large deviation theory is the study of the estimation and approximation of very small probabilities. These arise in the study of transmission errors in information communication, in studying large exceedances in random networks, in estimating failure probabilities in large systems (e.g. insurance companies) and many other settings. New techniques will be developed and applied to study the rate at which these probabilities decrease as the number of observations increases. A second subject to be studied is a model for electron-photon cascades, in particular, the ratio of the number of electrons to photons above a given energy level.

9625552 NEY抽象研究将在两个一般领域进行：大偏差理论和级联理论。 在大偏差理论中，将使用再生和更新方法来扩展子添加论证对马尔可夫添加剂过程和无限记忆链的适用性。 这产生了建立大偏差原理存在的快速而直接的方法。 将研究用于识别相关速率功能的新技术。 与无限顺序链有关的某些单调图的迭代元素的大偏差将是通过上述方法进行的。 电子 - 光子级联反应将作为多类分支随机步行的特殊情况进行研究。 将研究有关电子和在吸收剂大深度固定能量上方的电子和光子之间平衡的一个开放问题。 大偏差理论是对非常小概率的估计和近似的研究。 这些出现在信息通信中的传输错误，研究随机网络中的巨大超越，估计大型系统（例如保险公司）和许多其他许多环境中的失败概率时出现的。 将开发并应用新技术来研究这些概率随着观察次数的增加而降低的速率。 要研究的第二个受试者是电子 - 光子级联反应的模型，尤其是电子与给定能级高于给定能级的光子的比率。