Timeline for Hitting time of a stochastically continuous process
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 10, 2015 at 15:32 | comment | added | kenneth | For $\alpha$-stable process, it seems to me yes. From scaling property, for any $c>0$, we have $\max_{0\le t <c} |X_t| \sim c^{1/\alpha} \max_{0\le t <1} |X_t|$. This implies $P(\max_{0\le t <c} |X_t| <1) = P(\max_{0\le t <1} |X_t| < c^{-1/\alpha}) \to 1$ as $c\to 0$. Thus, $P(\tau>0) \ge P(\tau\ge c) = P(\max_{0\le t <c} |X_t| <1) \to 1$ as $c\to 1$. Thanks for your help. | |
| Nov 10, 2015 at 15:27 | comment | added | Serguei Popov | Sorry, I'm not a specialist in Levy processes :) | |
| Nov 10, 2015 at 15:01 | comment | added | kenneth | Thanks for this cute example. I am considering a Levy jump process, ex. $\alpha$-stable process for $\alpha = 3/2$. Is $\tau>0$ a.s.? Thanks. | |
| Nov 10, 2015 at 14:46 | vote | accept | kenneth | ||
| Nov 10, 2015 at 11:29 | history | answered | Serguei Popov | CC BY-SA 3.0 |