Mathematical Sciences: Applications and Refinements of the Theory of Large Deviations

本研究集中在扩展和细化的大型 偏差理论，特别是应用于 沟通与控制的问题，进行比较分析， 分子（DNA和蛋白质）序列，并涉及生物化学的研究。 过程和连续实验。 在预期的 结果是新的极限定理的分布条件 罕见事件的指数小概率，和小说 马尔可夫过程分段的经验规律分析， 马尔可夫随机场，通过适当的选择， 停车时间。 另一种有前途的新方法是基于使用 关联不等式（FKG类型）和交换不等式 作为获得大偏差范围的工具。 这些边界是 适用于时变参数的估计和 根据罕见事件概率比较抽样方案。 这项研究的中心是估计罕见的 发生的事件，在这些事件具有根本性意义的地区， 重要性 示例包括评估统计学显著性 不寻常的DNA序列片段组成，分析长 复杂排队系统中的等待时间， 并行计算机系统

This research centers on extensions and refinements of large deviations theory, especially motivated by applications to problems of communication and control, to comparative analysis of molecular (DNA and protein) sequences, and to studies of queueing processes and sequential experimentation. Among the expected results are new limit theorems for distributions conditioned on rare events of exponentially small probabilities, and the novel analysis of the empirical law of segments of Markov processes and Markov random fields that are selected by means of appropriate stopping times. Another promising new approach is based on using association inequalities (of the FKG type), and exchangeability as tools for obtaining large deviations bounds. These bounds are applicable for the estimation of time-varying parameters and for comparing sampling schemes in terms of rare events probabilities. This research centers on estimating the chances for rare events to occur, in areas where such events are of fundamental importance. Examples include assessing statistical significance of unusual DNA sequence segment compositions, analysis of long waiting times in complex queueing systems, and analysis of parallel computer systems.