Timeline for Bound from above and from below the probability that a 1-D centered random walk remains at each step inside a square root boundary
Current License: CC BY-SA 4.0
13 events
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| May 8 at 17:43 | comment | added | Ziv | @MathRevenge Is the sum the same as something like $P(I_1) + \sum_{n = 1} P(I_n)$? (Write $n = \sum_{k=1}^n 1$, then use Tonelli's theorem to swap the sums.) That would imply you only need to bound $P(I_n)$ from below. | |
| Apr 28 at 16:18 | comment | added | Iosif Pinelis | This goal should be, and should have been, stated explicitly in your post. | |
| Apr 28 at 16:09 | history | edited | MathRevenge | CC BY-SA 4.0 |
added 17 characters in body
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| Apr 28 at 16:04 | comment | added | MathRevenge | Unfortunately my goal is to show that, in my case, the series $\sum_{n=2}^{\infty}n(P(I_{n-1})-P(I_{n}))$ is divergent.. and in order to prove it I thought to bound that expression with a function $g(n)$ such that the series of $ng(n)$ is divergent. (If not, I otherwise have to show that the first series is convergent instead) | |
| Apr 28 at 14:37 | comment | added | Iosif Pinelis | Doesn't then your question reduce to this: show that $P(I_{n-1})-P(I_n)>0$ for all large enough $n$? | |
| Apr 28 at 14:22 | comment | added | MathRevenge | In the sense that in my case $X_i = \cos{\theta_i}$ where $\theta_i$ is uniformly distributed in $[0,2\pi]$. Maybe it could be useful.. | |
| Apr 28 at 13:55 | comment | added | Iosif Pinelis | You can provide the distribution of $X_1$? In what sense? | |
| Apr 28 at 13:48 | comment | added | MathRevenge | I mean, the distribution of $X_1$. I was not precise, sorry. | |
| Apr 28 at 13:31 | comment | added | Iosif Pinelis | You can provide what? | |
| Apr 28 at 13:23 | comment | added | MathRevenge | Not necessarily! If needed I can provide it. @IosifPinelis | |
| Apr 28 at 13:20 | comment | added | Iosif Pinelis | Do you want $g$ to be independent of the distribution of $X_1$? | |
| Apr 28 at 13:08 | history | edited | MathRevenge | CC BY-SA 4.0 |
edited tags
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| Apr 28 at 13:01 | history | asked | MathRevenge | CC BY-SA 4.0 |