Timeline for Friedrich's extension of the generator of a continuous time markov chaoin
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2020 at 22:47 | comment | added | Jochen Glueck | @MateuszKwaśnicki: I see, thank you very much! I sometimes tend to see things through my "semigroup filter" - so when I hear "Markov process with countable state space", I just think of a positive $C_0$-semigroup on $\ell^1$ which is norm-preserving on the positive cone. | |
| Apr 9, 2020 at 20:55 | comment | added | Mateusz Kwaśnicki | @JochenGlueck: That likely depends on your favourite definition of a Markov chain. As I understand, if we assume that the paths are càdlàg in the discrete topology on $\mathbb{Z}$, then the indicator functions are in the domain of the generator. | |
| Apr 7, 2020 at 22:43 | comment | added | Jochen Glueck | I just found this paper by Ornstein; in the middle of the first page, he claims that there are examples where not all the indicator functions $1_n$ are in the domain of $G$: "if $i=j$ there are examples where it [it = the derivative of the transition probability $P_{ij}(t)$ at $t=0$] is infinite". | |
| Apr 3, 2020 at 23:18 | comment | added | Jochen Glueck | Well yes, but my question is: why are all of these indicator functions in the domain? I'm not really convinced that this follows from your assumptions. (But I might be overlooking something simple or well-known.) | |
| Apr 3, 2020 at 21:39 | answer | added | Mateusz Kwaśnicki | timeline score: 1 | |
| Apr 3, 2020 at 21:02 | comment | added | Ribhu | I think it should be straight forward. Since the functions of the form $1_n$ (indicator functions) are in the domain, so is their span. | |
| Apr 3, 2020 at 19:54 | comment | added | Jochen Glueck | Thanks for your response! How do you know that $C_c(\mathbb{Z})$ is contained in the domain of $G$? | |
| Apr 3, 2020 at 19:40 | comment | added | Ribhu | Yes, it is the set of functions with finite support. I have edited it now. | |
| Apr 3, 2020 at 19:39 | history | edited | Ribhu | CC BY-SA 4.0 |
added 70 characters in body
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| Apr 3, 2020 at 19:25 | comment | added | Jochen Glueck | Could you specifiy what you mean by $C_c(\mathbb{Z})$? The functions with finite support? | |
| Apr 3, 2020 at 18:33 | history | asked | Ribhu | CC BY-SA 4.0 |