Timeline for Independent increments for the Brownian motion on a Riemannian manifold
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2020 at 18:57 | comment | added | Alex M. | @MartinHairer: Indeed, I am looking for a concept not only of theoretical value, but also of operational one, allowing me to juggle with formulae. So far, Riemannian homogeneous spaces fit the bill. Surprinsingly, though, I am unable to say anything about closed manifolds, even though these are among the nicest Riemannian objects. Maybe the plain Riemannian structure is too amorphous, and one really needs some supplementary algebraic structure allowing one to relate points to each other? | |
| Oct 2, 2020 at 18:28 | comment | added | Martin Hairer | @Alex Well, one generalisation is that harmonic functions (the analogue of the coordinate functions) are martingales (the analogue of having independent increments), but that may not be terribly useful for you... | |
| Oct 2, 2020 at 8:32 | comment | added | Mateusz Kwaśnicki | Ah, sorry, I thought "homogeneous space" means something else. | |
| Oct 2, 2020 at 8:31 | comment | added | Alex M. | @MateuszKwaśnicki: I know that, this is why I am asking about a substitute. Yes, as I have said, I know how to do it on Riemannian homogeneous spaces. | |
| Oct 2, 2020 at 8:30 | history | edited | Alex M. | CC BY-SA 4.0 |
added 29 characters in body
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| Oct 2, 2020 at 8:30 | comment | added | Mateusz Kwaśnicki | I believe $c(s')-c(s)$ makes no sense for a general manifold $M$. If $M$ is a Lie group (or perhaps a symmetric space), however, then you are good to go. | |
| Oct 2, 2020 at 8:26 | history | asked | Alex M. | CC BY-SA 4.0 |