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
相关论文
共 50 条
  • [1] On multiplicatively closed subsets of normed algebras
    Moreno Galindo, Antonio
    Rodriguez Palacios, Angel
    JOURNAL OF ALGEBRA, 2010, 323 (05) : 1530 - 1552
  • [2] On the Killing form on Lie Algebras
    V. V. Gorbatsevich
    Russian Mathematics, 2021, 65 : 44 - 60
  • [3] On the Killing form on Lie Algebras
    Gorbatsevich, V. V.
    RUSSIAN MATHEMATICS, 2021, 65 (04) : 44 - 60
  • [4] Lie Markov models
    Sumner, J. G.
    Fernandez-Sanchez, J.
    Jarvis, P. D.
    JOURNAL OF THEORETICAL BIOLOGY, 2012, 298 : 16 - 31
  • [5] Closed form PHD filtering for linear jump markov models
    Pasha, A.
    Vo, B.
    Tuan, H. D.
    Ma, W. -K.
    2006 9TH INTERNATIONAL CONFERENCE ON INFORMATION FUSION, VOLS 1-4, 2006, : 240 - 247
  • [6] Closed form of the Baker–Campbell–Hausdorff formula for the generators of semisimple complex Lie algebras
    Marco Matone
    The European Physical Journal C, 2016, 76
  • [7] REDUCTIVITY OF CERTAIN LIE-ALGEBRAS ASSOCIATED WITH CLOSED DIFFERENTIAL 2-FORM
    DIAZMIRA.A
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1973, 276 (06): : 483 - 485
  • [8] Closed-form likelihood function of Markov-switching models
    Yang, MX
    ECONOMICS LETTERS, 2001, 70 (03) : 319 - 326
  • [9] LIE ALGEBRAS WITH A QUOTIENT TRACE FORM
    BLOCK, RE
    ILLINOIS JOURNAL OF MATHEMATICS, 1965, 9 (02) : 277 - &
  • [10] Closed form of the Baker-Campbell-Hausdorff formula for the generators of semisimple complex Lie algebras
    Matone, Marco
    EUROPEAN PHYSICAL JOURNAL C, 2016, 76 (11):
12345