Timeline for Definition of random measures
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 8, 2023 at 21:14 | vote | accept | Henning | ||
| Feb 22, 2020 at 15:56 | history | edited | Henning | CC BY-SA 4.0 |
added 628 characters in body
|
| Feb 22, 2020 at 15:34 | answer | added | Henning | timeline score: 1 | |
| Feb 22, 2020 at 9:57 | history | edited | Henning |
edited tags
|
|
| Feb 22, 2020 at 1:08 | comment | added | Julian Newman | I think it might be good to add the descriptive set theory tag to the list of tags. | |
| Feb 22, 2020 at 1:07 | answer | added | Julian Newman | timeline score: 7 | |
| Feb 21, 2020 at 23:16 | comment | added | Henning | @ Nate Eldredge: e.g. Kallenberg's books (Random Measures (1974), www4.stat.ncsu.edu/~boos/library/mimeo.archive/…, Foundations of Modern Probability Theory (2002), Random Measures and Applications (2017) ) and also tDaley and Vere-Jones "Introduction to the Theory of Point Processes" Vol. II other textbooks just use $\mathbb{R}^k$ or certain subsets | |
| Feb 21, 2020 at 23:08 | comment | added | Mateusz Kwaśnicki | I think sometimes people use more general random measures. For example, Poisson point process of excursions (of a Markov process) is a random measure with values in the Skorohod space, a Polish space which is not locally compact. That said, weak convergence of measures is much simpler on locally compact Polish spaces. And I think it gets very difficult to work with on non-separable metric spaces. | |
| Feb 21, 2020 at 22:52 | comment | added | Nate Eldredge | I think it may depend in part on what one wants to do with the random measure. Do you have some examples of textbooks where you've seen this, so we could see what the context is? | |
| Feb 21, 2020 at 22:25 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title, formatting
|
| Feb 21, 2020 at 22:01 | comment | added | Henning | Thanks for the link! Actually I already have a $\sigma$-algebra, that is, I implicitly consider the $\sigma$-algebra on the set of all measures on $(X,\mathcal{B})$ that is generated by the evaluation maps $\mu \mapsto \mu(B)$ for all $B\in\mathcal{B}$ | |
| Feb 21, 2020 at 21:50 | comment | added | Robert Furber | If you want a $\sigma$-algebra for the set of probability measures on a measurable space, you are looking for this: ncatlab.org/nlab/show/Giry+monad | |
| Feb 21, 2020 at 20:30 | history | asked | Henning | CC BY-SA 4.0 |