The comonotone flow of a stochastically monotone Feller process on the real line
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918244874452992 |
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| author | Bérard, Jean Frénais, Brieuc |
| author_facet | Bérard, Jean Frénais, Brieuc |
| contents | We show that any stochastically monotone Feller semigroup on R can be extended by a consistent family of order-preserving Feller semigroups on the successive powers of R. We exhibit a specific such family, which is uniquely characterized by a maximality property with respect to the super-modular order on Rn. A consequence is that, in this fairly general setting, there always exists a coupling between n c{à}dl{à}g versions of the underlying Markov process starting from n distinct initial positions, which do not cross one another. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18391 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The comonotone flow of a stochastically monotone Feller process on the real line Bérard, Jean Frénais, Brieuc Probability We show that any stochastically monotone Feller semigroup on R can be extended by a consistent family of order-preserving Feller semigroups on the successive powers of R. We exhibit a specific such family, which is uniquely characterized by a maximality property with respect to the super-modular order on Rn. A consequence is that, in this fairly general setting, there always exists a coupling between n c{à}dl{à}g versions of the underlying Markov process starting from n distinct initial positions, which do not cross one another. |
| title | The comonotone flow of a stochastically monotone Feller process on the real line |
| topic | Probability |
| url | https://arxiv.org/abs/2311.18391 |