Providing sufficient conditions for at most one stationary probability measure in countable state spaces, suggesting insights into infinite order chains.
In this paper, we consider chains of infinite order on countable state spaces with prohibited transitions. We give a set of sufficient conditions on the structure of the probability kernels of the chains to have at most one stationary probability measure compatible with the kernel. Our main result extends the uniqueness ² criterion from Johansson and Öberg (2003) which was obtained for strongly non-null chains. A particular attention is given to concrete examples, illustrating the main theorem and its corollaries, with comparison to results of the existing literature.
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Gallesco et al. (2025) studied this question.
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