On finite interweaving relations
Résumé
An interweaving relation is a Markovian similarity-type relation between two Markov chains introducing a warming-up time after which
their time-marginal distributions can be tightly compared (for different initial distributions).
For non-transient Markov transition kernels on the same state space, these relations are shown to be equivalent to the usual similarity relation. Some bounds are deduced on corresponding warming-up times, when the eigenvalues are furthermore assumed to be real.
When the eigenvalues are non-negative, the same approach enables us to construct strong stationary times for irreducible Markov chains through interweaving relations with model absorbed Markov chains, thus extending a result due to Matthews in the reversible situation.
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