Embedding of sub-stochastic matrices
Michael Baake, Kiah Swinsburg
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≤slant 3.
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