MULTIPLICATIVELY CLOSED MARKOV MODELS MUST FORM LIE ALGEBRAS

被引：8
|
作者：
Sumner, Jeremy G. [1 ]
机构：
[1] Univ Tasmania, Hobart, Tas 7000, Australia
来源：
ANZIAM JOURNAL | 2017年 / 59卷 / 02期
基金：
澳大利亚研究理事会;
关键词：
Lie algebras; continuous-time Markov chains; semigroups; phylogenetics;
D O I：
10.1017/S1446181117000359
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the probability substitution matrices obtained from a continuous-time Markov chain form a multiplicatively closed set if and only if the rate matrices associated with the chain form a linear space spanning a Lie algebra. The key original contribution we make is to overcome an obstruction, due to the presence of inequalities that are unavoidable in the probabilistic application, which prevents free manipulation of terms in the Baker-Campbell-Haursdorff formula.
引用
收藏
页码：240 / 246
页数：7
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