Uniqueness of stationary compatible probability measures for chains of infinite order with forbidden transitions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911703759847424 |
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| author | Gallesco, Christophe Gallo, Sandro Takahashi, Daniel Yasumasa |
| author_facet | Gallesco, Christophe Gallo, Sandro Takahashi, Daniel Yasumasa |
| contents | 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 $\ell^2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of stationary compatible probability measures for chains of infinite order with forbidden transitions Gallesco, Christophe Gallo, Sandro Takahashi, Daniel Yasumasa Probability Dynamical Systems 60G10, 60G99 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 $\ell^2$ 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. |
| title | Uniqueness of stationary compatible probability measures for chains of infinite order with forbidden transitions |
| topic | Probability Dynamical Systems 60G10, 60G99 |
| url | https://arxiv.org/abs/2507.16981 |