Timeline for Comparison of probabilities that drifted Brownian motion never hits barriers
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 10, 2021 at 6:27 | vote | accept | GJC20 | ||
| Oct 10, 2021 at 4:06 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Oct 9, 2021 at 16:50 | comment | added | Yuval Peres | I deleted my comment. | |
| Oct 9, 2021 at 16:49 | comment | added | GJC20 | @YuvalPeres I think $\lim_{t\to\infty}X^k_t=\infty$ with $X^k_t:=2+\beta t+W_t-k(t)$, while $\mathbb P[\tau_k=\infty]=\mathbb P[X^k_t>0, \forall t\ge 0]>1$ | |
| Oct 9, 2021 at 16:44 | comment | added | GJC20 | @ChristianRemling Thanks for the hint. I think I know how to prove the strict inequality | |
| Oct 8, 2021 at 17:12 | comment | added | Christian Remling | You also have $k(t)\le a<b\le h(t)$ on a suitable time interval, and the probability of hitting $(a,b)$ during that interval is non-zero. | |
| Oct 8, 2021 at 16:32 | history | asked | GJC20 | CC BY-SA 4.0 |