Timeline for Lower bounding the infimum of a random process
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2023 at 20:26 | vote | accept | tony | ||
| Jul 17, 2023 at 12:49 | comment | added | Iosif Pinelis | It is not true that $\inf_{t\in T} X_t=0$. What is true (and shown in the answer) is that $\inf_{t\in T} X_t\le0$, which immediately implies (as stated in the answer) that $P(\inf X_t>0)=0\not\to1.$ | |
| Jul 17, 2023 at 8:55 | comment | added | tony | Thanks! but from $\inf X_t=0$, we can still say $P(\inf X_t\geq 0)\neq 0$, and then since $P(\inf X_t>0)=P(\inf X_t\geq 0)$ (if I am correct), we cannot conclude $P(\inf X_t>0)= 0$. | |
| Jul 16, 2023 at 16:31 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |