Timeline for Probability of a Random Walk crossing an increasing function of the standard deviation
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2012 at 21:30 | comment | added | Ori Gurel-Gurevich | I suggest taking a look at how the LIL is derived, then trying to apply similar methods for your problem. In general, you want to measure the correlation between the events $S_i > h(i)$, and it is often useful to bunch all of these events for $i=2^j,..,2^{j+1}$ together. the correlation between different $j$'s here will then decay exponentially. | |
| Apr 30, 2012 at 20:42 | comment | added | TMM | Thanks, that looks very interesting. But I'm also interested in an "efficient" way to turn the $\mathcal{P}_h(n)$ above into something nicer. Of course we could use the upper bound $P(\exists \ n_0 \leq n: S_{n_0} > h(n_0)) \leq \sum_{i=1}^n P(S_i > h(i))$ but that does not seem very sharp. | |
| Apr 30, 2012 at 19:45 | history | answered | Ori Gurel-Gurevich | CC BY-SA 3.0 |