A Generalization of L\'evy's Theorem on Positive Matrix Semigroups
Functional Analysis
2024-03-19 v2 Probability
Abstract
We generalize a fundamental theorem on positive matrix semigroups stating that each component is either strictly positive for all times or identically zero ("L\'evy's Theorem"). Our proof of this fact that does not require the matrices to be Markovian nor to be continuous at time zero. We also provide a formulation of this theorem in the terminology of one-parameter operator semigroups on sequence spaces.
Cite
@article{arxiv.2401.03487,
title = {A Generalization of L\'evy's Theorem on Positive Matrix Semigroups},
author = {Moritz Gerlach},
journal= {arXiv preprint arXiv:2401.03487},
year = {2024}
}
Comments
10 pages, 0 figures; this is version 2, the title has been changed in addition to a revision of section 3