Timeline for A Kolmogorov inequality for sums of contiguous subsequences
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 21 at 20:39 | comment | added | Rob Arthan | @IosifPinelis: sure! thanks for all your time on what turned out to be a diversion which turned out not to be relevant to my current problem but may perhaps help others. | |
| Feb 21 at 16:31 | comment | added | Iosif Pinelis | You also had $\lambda$ going to $0$, rather than $\infty$. So, whatever the value of the original or changed question may be, the post should not be deleted. | |
| Feb 21 at 16:10 | comment | added | Rob Arthan | Apologies, there was a repeated and highly significant typo in the above: "${} < \lambda$" should read "${} > \lambda$" throughout. What we were looking for is an upper bound, tending to $0$ as $\lambda \to \infty$ on $P[\max_{1\le j < k \le n}[|S_k - S_j| > \lambda]$. That turns out to be easier to find that we thought at first (using the Kolmogorov and triangle inequalities), so I am happy with the answer given below, as it resolves the original (unintended) question. | |
| Feb 21 at 14:22 | comment | added | Iosif Pinelis | You should not change the question, especially so drastically, especially after an answer was given (which you gratefully accepted). | |
| Feb 21 at 13:52 | history | edited | Rob Arthan | CC BY-SA 4.0 |
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| Feb 21 at 13:50 | comment | added | Rob Arthan | In fact, I think the amended question actually follows easily from the Kolmogorov inequality and the triangle inequality. So I think I'lll delete this question as I don't think it adds much value to MO users. | |
| Feb 21 at 13:32 | history | edited | Rob Arthan | CC BY-SA 4.0 |
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| Feb 21 at 13:13 | history | edited | Rob Arthan | CC BY-SA 4.0 |
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| Feb 21 at 13:08 | history | edited | Rob Arthan | CC BY-SA 4.0 |
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| Feb 19 at 20:55 | comment | added | Rob Arthan | @IosifPinelis: I have changed the notation in the question. | |
| Feb 19 at 20:55 | history | edited | Rob Arthan | CC BY-SA 4.0 |
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| Feb 19 at 20:52 | comment | added | Iosif Pinelis | It is not a good idea to use $\Bbb P$ and $\Bbb E$ to denote the probability and the expectation; use $P,E$ or $\mathsf P,\mathsf E$ instead. Blackboard bold is reserved for $\Bbb R$, $\Bbb C$, $\Bbb Z$, and other similar sets. | |
| Feb 19 at 20:51 | vote | accept | Rob Arthan | ||
| Feb 19 at 20:48 | comment | added | Iosif Pinelis | Kolmorogov's maximal inequality provides a lower bound on $P(\max_{1\le k \le n}|S_k| < \lambda)$. | |
| Feb 19 at 20:47 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Feb 19 at 20:27 | history | asked | Rob Arthan | CC BY-SA 4.0 |