Some geometric properties of stochastic matrices

Cristian F. Coletti, Rafael P. Carneiro, Sandra Z. Yepes

Resumo


We study geometric aspects of transition matrices of discrete-time Markov chains. More precisely, we study the connected component of the set of stochastic matrices with positive determinant at the identity. Using the machinery of Lie groups we explore the connection between stochastic matrices and transition rate matrices.

Palavras-chave


Discrete-time Markov chains, Continuous-time Markov chains, Stochastic matrices, Lie group, Lie algebra.

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DOI: https://doi.org/10.5540/03.2020.007.01.0439

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