An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator
A Markov matrix is embeddable if it can represent a homogeneous continuous-time Markov process. It is well known that if a Markov matrix has real and pairwise-different eigenvalues, then the embeddability can be determined by checking whether its principal logarithm is a rate matrix or not. The same...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/366197 |
| Acceso en línea: | https://hdl.handle.net/2117/366197 https://dx.doi.org/10.1080/03081087.2020.1854165 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebras, Linear Multilinear algebra Matrices Markov processes Markov matrix Markov generator Embedding problem Rate identifiability Àlgebra lineal Àlgebra multilineal Matrius (Àlgebra) Markov, Processos de Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica |
| Sumario: | A Markov matrix is embeddable if it can represent a homogeneous continuous-time Markov process. It is well known that if a Markov matrix has real and pairwise-different eigenvalues, then the embeddability can be determined by checking whether its principal logarithm is a rate matrix or not. The same holds for Markov matrices that are close enough to the identity matrix. In this paper we exhibit open sets of Markov matrices that are embeddable and whose principal logarithm is not a rate matrix, thus proving that the principal logarithm test above does not suffice generically. |
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