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.
Funding
Australian Research Council
History
Publication title
ANZIAM Journal
Volume
59
Pagination
240-246
ISSN
1446-1811
Department/School
School of Natural Sciences
Publisher
Australian Mathematics Publ Assoc Inc
Place of publication
Mathematics Dept Australian National Univ, Canberra, Australia, Act, 0200