Timeline for Martingales converging in probability but not a.s
Current License: CC BY-SA 4.0
16 events
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| Dec 10, 2021 at 21:47 | comment | added | Bill Johnson | For me, Iosif, it is be more sympathetic to students who do not read the text book as I have taught from Durrett's book. | |
| Dec 9, 2021 at 18:24 | comment | added | Iosif Pinelis | @GuillaumeAubrun : Thank you for your comment. (This is Example 4.2.14 in the version of the book at services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf .) That example is indeed much simpler. I thought of something like this for a moment, but it did not occur to me how to nullify $X_n$ in just one step. Well, this turns out very easy to do. The lesson for me: read textbooks. :-) | |
| Dec 9, 2021 at 17:58 | comment | added | Guillaume Aubrun | @BillJohnson in the current generation of books, a counterexample (arguably simpler) appears as Example 5.2.4 in Rick Durett's "Probability: Theory and examples" | |
| Dec 9, 2021 at 17:44 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 9, 2021 at 17:31 | comment | added | Iosif Pinelis | @BillJohnson : Thank you for your comment. | |
| Dec 9, 2021 at 16:09 | comment | added | Bill Johnson | An example of this phenomenon should be in the next generation of books that treat martingale theory. | |
| Dec 9, 2021 at 15:18 | comment | added | Iosif Pinelis | @LiviuNicolaescu : Thank you for your comment. | |
| Dec 9, 2021 at 15:18 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 9, 2021 at 14:42 | vote | accept | Liviu Nicolaescu | ||
| Dec 9, 2021 at 13:49 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 9, 2021 at 13:22 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 9, 2021 at 10:40 | comment | added | Liviu Nicolaescu | Splendid example! | |
| Dec 9, 2021 at 5:00 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 8, 2021 at 22:24 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 8, 2021 at 21:40 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Dec 8, 2021 at 21:04 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |