On the algebra of equal-input matrices in time-inhomogeneous Markov flows
Probability
2025-04-16 v2 Classical Analysis and ODEs
Abstract
Markov matrices of equal-input type constitute a widely used model class. The corresponding equal-input generators span an interesting subalgebra of the real matrices with zero row sums. Here, we summarise some of their amazing properties and discuss the corresponding Markov embedding problem, both homogeneous and inhomogeneous in time. In particular, we derive exact and explicit solutions for time-inhomogeneous Markov flows with non-commuting generator families of equal-input type and beyond.
Keywords
Cite
@article{arxiv.2404.11222,
title = {On the algebra of equal-input matrices in time-inhomogeneous Markov flows},
author = {Michael Baake and Jeremy Sumner},
journal= {arXiv preprint arXiv:2404.11222},
year = {2025}
}
Comments
18 pages, with an appendix on Peano--Baker series and Magnus expansion; slightly revised and improved version