On the existence of Markovian measures on continuous paths
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910267464482816 |
|---|---|
| author | Pitcho, Jules |
| author_facet | Pitcho, Jules |
| contents | Let $\mathbfη$ be a positive Radon measure on the space of continuous paths from R into a locally compact Polish space $Y$, and assume that $\mathbfη$ admits an invariant measure. We explicit conditions on $\mathbfη$ such that successive Markovianisation of $\mathbfη$ over any dense and countable set of times have all limit points (in the weak-star topology on Radon measures) satisfying the strong Markov property. We show that if Y is a locally compact Polish group, and $\mathbfη$ is left or right translation invariant, then $\mathbfη$ satisfies such conditions. Our proof uses the Zermalo-Fraenkel and Axiom of Dependant Choice axiomatisation of set theory, in which countable products of compacts are compact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the existence of Markovian measures on continuous paths Pitcho, Jules Analysis of PDEs Mathematical Physics Probability 60B05, 60J99, 76F05, 76F25 Let $\mathbfη$ be a positive Radon measure on the space of continuous paths from R into a locally compact Polish space $Y$, and assume that $\mathbfη$ admits an invariant measure. We explicit conditions on $\mathbfη$ such that successive Markovianisation of $\mathbfη$ over any dense and countable set of times have all limit points (in the weak-star topology on Radon measures) satisfying the strong Markov property. We show that if Y is a locally compact Polish group, and $\mathbfη$ is left or right translation invariant, then $\mathbfη$ satisfies such conditions. Our proof uses the Zermalo-Fraenkel and Axiom of Dependant Choice axiomatisation of set theory, in which countable products of compacts are compact. |
| title | On the existence of Markovian measures on continuous paths |
| topic | Analysis of PDEs Mathematical Physics Probability 60B05, 60J99, 76F05, 76F25 |
| url | https://arxiv.org/abs/2605.29036 |