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arXiv · 2608.03338

Embedding of sub-stochastic matrices

Michael Baake·Kiah Swinsburg
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Abstract

The classic embedding problem for finite-dimensional Markov matrices has a natural counterpart for sub-stochastic matrices, which is analysed and discussed here. One necessary and sufficient characterisation of embeddability can be given via the unique extension of a sub-stochastic matrix to a stochastic one with one added state in conjunction with the embedding of this extension. This is then explicitly treated for $d\leqslant 3$.

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Michael Baake, Kiah Swinsburg. 2026-08-04. Embedding of sub-stochastic matrices. https://arxiv.org/abs/2608.03338

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