Distribution theory of runs and patterns and its applications

游程和模式的分布理论及其应用

• 批准号: 9216-2010
• 负责人: Fu, James
• 金额: $ 1.09万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=544608
• 关键词: Distribution; theory; runs; patterns; its

In a sequence of previous projects and publications, a simple and powerful method known as "finite Markov chain imbedding" was developed to compute the exact probabilities of waiting times and occurrences for the number of words, patterns, or runs in a sequence of symbols. The technique has had a high impact in both statistics and applied probability and has been used successfully in many areas, such as reliability theory, quality control, DNA sequence analysis, psychology, astronomy, statistics, and biology. This five-year research proposal deals with further refinements to this method, and contains four parts: (i) developing a better approximation for the distribution of complex words, runs and patterns, (ii) extending Markov chain imbedding to study the boundary crossing probability for Brownian motion and its related processes, (iii) using the method to examine the distribution of clusters in DNA sequences and hospital ER wait times(a hot issue in Canada), and (iv) applying the results from (ii) to study bankruptcy and financial distress among large companies to avoid the recession as current one.

在之前的一系列项目和出版物中，开发了一种简单而强大的方法，称为“有限马尔可夫链嵌入”，用于计算等待时间和出现的确切概率，以及符号序列中单词，模式或运行的数量。 该技术在统计学和应用概率方面都产生了很大的影响，并已成功地应用于许多领域，如可靠性理论，质量控制，DNA序列分析，心理学，天文学，统计学和生物学。 这份为期五年的研究建议涉及对这一方法的进一步改进，包括四个部分：（i）对复杂的词、串和模式的分布提出了一个更好的近似;（ii）扩展马尔可夫链嵌入以研究布朗运动及其相关过程的边界穿越概率;（iii）使用该方法来检查DNA序列中簇的分布和医院ER等待时间（加拿大的一个热点问题），（iv）应用（ii）的结果来研究大公司的破产和财务困境，以避免当前的经济衰退。