关于矩阵族的一致相随性探讨

矩阵的对角化问题是高等代数中一个重要而基本的内容,通常文献只讨论一个给定方阵的可对角化条件。但在理论与应用中往往会大量涉及矩阵族的同时三角化问题。因此,研究矩阵族可同时三角化的条件将是一个不可回避的课题。另外有文献虽引入了相似矩阵可同时对角化的概念及判定条件,但实际上矩阵族同时三角化和同时对角化在论证上差异却很大。为此,在已有研究的基础上,引入了矩阵族的一致相随定义,利用特征分析技术研究了矩阵族可同时三角化问题,得到了一致相随存在性的一个定理及其证明,最后例举了一致相随关系的两个应用。

Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate

Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.