Timeline for $P(\max_{1 \leq p \leq k}|Y_p| >\epsilon) \geq 1-4\frac{(\epsilon+\max_{1 \leq p \leq k } |X_p-E[X_p]|)^2}{\operatorname{Var}(Y_k)}$
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12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2021 at 18:54 | vote | accept | Kurt.W.X | ||
| Apr 28, 2021 at 17:21 | comment | added | Kurt.W.X | A "variant" of Hoffmann–Jørgensen inequality can be also found amazon.com/… page 115, by introducing a stopping time | |
| Apr 28, 2021 at 17:08 | comment | added | Iosif Pinelis | I now see why Chung calls that theorem 'brutal". Unfortunately, he does not mention the mistake in Kolmogorov's proof. Anyhow, the Hoffmann–Jørgensen inequality seems more natural, more effective, and easier to prove. | |
| Apr 28, 2021 at 16:31 | comment | added | Kurt.W.X | pages 123-124 (theorem 5.3.2 and its proof) | |
| Apr 28, 2021 at 16:29 | comment | added | Kurt.W.X | Here's the link for google books: books.google.com.lb/… | |
| Apr 28, 2021 at 16:26 | comment | added | Kurt.W.X | I can post a picture - pdf file for the page from Chung books (because in Google books - amazon... it only shows a preview for the book and it happens that the page from where theorem 5.3.2 is taken is not omitted) | |
| Apr 28, 2021 at 16:18 | comment | added | Iosif Pinelis | @Kurt.W.X : I see "Finally, and this is mentioned here only in response to a query by Doob, I chose to present the brutal Theorem 5.3.2 in the original form given by Kolmogorov because I want to expose the student to hardships in mathematics." on p.434 at play.google.com/books/… . Can you give me a link to the Google book by Chung? I cannot find it right away. | |
| Apr 28, 2021 at 16:14 | comment | added | Kurt.W.X | The funny thing is that inequality $(1)$ and the symmetric argument are asked in the exercises right after this section | |
| Apr 28, 2021 at 16:07 | comment | added | Kurt.W.X | After running a search on the above publication (google books), it appears that Kai Lai Chung (A course in probability theory, third edition) use inequality $(2)$ (the correct version) and he provided a proof (it's theorem 5.3.2).. | |
| Apr 28, 2021 at 15:25 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Apr 28, 2021 at 15:12 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Apr 28, 2021 at 5:57 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |