Representation of Markov chains by random maps: existence and regularity conditions
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2012
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910480140861440 |
|---|---|
| author | Jost, Jürgen Kell, Martin Rodrigues, Christian S. |
| author_facet | Jost, Jürgen Kell, Martin Rodrigues, Christian S. |
| contents | We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1207_5003 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Representation of Markov chains by random maps: existence and regularity conditions Jost, Jürgen Kell, Martin Rodrigues, Christian S. Dynamical Systems Differential Geometry Probability 37C40, 49K45, 49N60 (Primary), 37H10, 37C05 (Secondary) We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms. |
| title | Representation of Markov chains by random maps: existence and regularity conditions |
| topic | Dynamical Systems Differential Geometry Probability 37C40, 49K45, 49N60 (Primary), 37H10, 37C05 (Secondary) |
| url | https://arxiv.org/abs/1207.5003 |