Timeline for If a strong Markov process reaches a Borel set a.s., can it be restarted from that set?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 17, 2019 at 12:47 | answer | added | Mateusz Kwaśnicki | timeline score: 3 | |
| Apr 17, 2019 at 10:18 | comment | added | Mateusz Kwaśnicki | Thanks for clarification, now I see. And you are right, I was too fast with my comment in brackets. | |
| Apr 17, 2019 at 10:09 | comment | added | user1118 | Another question on this site comes tantalisingly close: For any $\varepsilon>0$ I can find a stopping time $T$ such that $P_x(X_T\in B)>1-\varepsilon$. mathoverflow.net/questions/50154/… | |
| Apr 17, 2019 at 10:08 | comment | added | user1118 | $E$ is a locally compact, separable metric space (but I'd be happy with an answer for $\mathbb R$). No càdlàg paths, although if that assumption makes a difference then I'd be interested to see how. Theorem I.11.4 in Blumenthal and Getoor's book on Markov processes gives me that at the first hitting time of $B$, $X$ is either in $B$ or at a point that is regular for $B$. | |
| Apr 17, 2019 at 9:57 | comment | added | Mateusz Kwaśnicki | What are the assumptions on $X$, $E$ and the underlying filtration? For example, do we require cádlág paths? More generally: are you interested in the generic, regular scenario (in which case the first hitting time of $B$ is a stopping time, and $X_T \in B$ by quasi-left continuity), or rather some exotic counterexamples? | |
| Apr 17, 2019 at 9:30 | review | First posts | |||
| Apr 17, 2019 at 10:01 | |||||
| Apr 17, 2019 at 9:27 | history | asked | user1118 | CC BY-SA 4.0 |