Timeline for Lower bounding the probability that a zero-mean sequence of random variables stays positive
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 10, 2020 at 18:56 | comment | added | Thomas Dybdahl Ahle | Very cool, so basically we use the Markov like inequality $E[f(X)] \ge \Pr[0 \le x\le r] \min_{0\le x \le r} f(x)$ for a cleverly chosen $f$. | |
| Mar 8, 2016 at 16:29 | comment | added | passerby51 | Here is another observation which is intriguing: The lower bound is decreasing in $t$ while the probably (LHS) is increasing, so it seems the bound is good for small values of $t$. With $a = (1+\sqrt{2})/2$, the lower bound seems to be maximized at $t = 3a/2$. So for all $t > 3a/2$, we should just use the bound for $t = 3a/2$. | |
| Mar 8, 2016 at 15:48 | comment | added | passerby51 | Thanks. This is interesting. I am intrigued by the word "standard". In what context is this standard? (I thought anything involving a cubic polynomial is fairly nonstandard!) | |
| Mar 7, 2016 at 22:42 | history | answered | Robert Israel | CC BY-SA 3.0 |