Timeline for Law of the iterated logarithm in Hilbert space
Current License: CC BY-SA 4.0
8 events
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| Oct 7, 2020 at 20:25 | comment | added | Iosif Pinelis | @Wolfgang : I don't know if the condition $E|X|^2<\infty$ is necessary here. I see that your posted question "Is there a corresponding result" did not say anything about minimal assumptions. | |
| Oct 7, 2020 at 16:56 | comment | added | Wolfgang | Thank you again. About minimal moment assumptions, on the real line, the second moment is necessary and sufficient for the law of the iterated logarithm to hold. Do I understand correctly that it is the same in Hilbert space with the condition E(|X|^2) finite? | |
| Oct 7, 2020 at 15:27 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 7, 2020 at 15:24 | comment | added | Iosif Pinelis | @Wolfgang : I have added details showing that your one-dimensional law of the iterated logarithm extends almost literally to Hilbert spaces. | |
| Oct 7, 2020 at 15:21 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 7, 2020 at 8:46 | comment | added | Wolfgang | Thank you for the reference. I would be also interested in the minimal assumptions for such a property to hold. | |
| Oct 6, 2020 at 14:37 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 6, 2020 at 14:28 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |