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Uniqueness of stationary compatible probability measures for chains of infinite order with forbidden transitions

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  • Gallesco, C.
  • Gallo, S.
  • Takahashi, D.Y.

Abstract

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 ℓ2 criterion from [1] 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.

Suggested Citation

  • Gallesco, C. & Gallo, S. & Takahashi, D.Y., 2026. "Uniqueness of stationary compatible probability measures for chains of infinite order with forbidden transitions," Stochastic Processes and their Applications, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:spapps:v:199:y:2026:i:c:s0304414926001262
    DOI: 10.1016/j.spa.2026.104994
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