Visible absorbing decompositions and uniqueness of invariant probabilities
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918494805688320 |
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| author | Attali, Jean-Gabriel |
| author_facet | Attali, Jean-Gabriel |
| contents | We identify the measurable absorbing obstruction to uniqueness of invariant probability measures for a Markov kernel. Ordinary absorbing decompositions obstruct global irreducibility and recurrence, but not necessarily uniqueness: an absorbing component may have full mass for no invariant probability.
We prove that a Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition, namely two disjoint absorbing sets, each having full mass for an invariant probability. The proof uses only the Jordan decomposition of the difference of two invariant probabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04900 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Visible absorbing decompositions and uniqueness of invariant probabilities Attali, Jean-Gabriel Mathematical Finance Probability We identify the measurable absorbing obstruction to uniqueness of invariant probability measures for a Markov kernel. Ordinary absorbing decompositions obstruct global irreducibility and recurrence, but not necessarily uniqueness: an absorbing component may have full mass for no invariant probability. We prove that a Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition, namely two disjoint absorbing sets, each having full mass for an invariant probability. The proof uses only the Jordan decomposition of the difference of two invariant probabilities. |
| title | Visible absorbing decompositions and uniqueness of invariant probabilities |
| topic | Mathematical Finance Probability |
| url | https://arxiv.org/abs/2601.04900 |