Most probable paths for developed processes
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908894832361472 |
|---|---|
| author | Grong, Erlend Sommer, Stefan |
| author_facet | Grong, Erlend Sommer, Stefan |
| contents | Optimal paths for the classical Onsager-Machlup function determining most probable paths between points on a manifold are only explicitly identified for specific processes, for example the Riemannian Brownian motion. This leaves out large classes of manifold-valued processes such as processes with parallel transported non-trivial diffusion matrix, processes with rank-deficient generator and sub-Riemannian processes, and push-forwards to quotient spaces. In this paper, we construct a general approach to definition and identification of most probable paths by measuring the Onsager-Machlup function on the anti-development of such processes. The construction encompasses large classes of manifold-valued process and results in explicit equation systems for the paths that we denote \emph{development most probable paths}. We define and derive these results and apply them to several cases of stochastic processes on Lie groups, homogeneous spaces, and landmark spaces appearing in shape analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_15168 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Most probable paths for developed processes Grong, Erlend Sommer, Stefan Probability Differential Geometry Statistics Theory 62R30, 60D05, 53C17 Optimal paths for the classical Onsager-Machlup function determining most probable paths between points on a manifold are only explicitly identified for specific processes, for example the Riemannian Brownian motion. This leaves out large classes of manifold-valued processes such as processes with parallel transported non-trivial diffusion matrix, processes with rank-deficient generator and sub-Riemannian processes, and push-forwards to quotient spaces. In this paper, we construct a general approach to definition and identification of most probable paths by measuring the Onsager-Machlup function on the anti-development of such processes. The construction encompasses large classes of manifold-valued process and results in explicit equation systems for the paths that we denote \emph{development most probable paths}. We define and derive these results and apply them to several cases of stochastic processes on Lie groups, homogeneous spaces, and landmark spaces appearing in shape analysis. |
| title | Most probable paths for developed processes |
| topic | Probability Differential Geometry Statistics Theory 62R30, 60D05, 53C17 |
| url | https://arxiv.org/abs/2211.15168 |