Timeline for Vector martingale concentration
Current License: CC BY-SA 3.0
6 events
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| Nov 30, 2017 at 23:03 | history | edited | Nikolayevich | CC BY-SA 3.0 |
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| Nov 30, 2017 at 22:56 | history | edited | Nikolayevich | CC BY-SA 3.0 |
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| Nov 30, 2017 at 11:30 | comment | added | Davide Giraudo | It seems indeed that Theorem 3.5 in Pinelis, Iosif Optimum bounds for the distributions of martingales in Banach spaces. (English summary) Ann. Probab. 22 (1994), no. 4, 1679–1706. is all what you need, as $\mathbb R^d$ endowed with the Euclidian is $(2,1)$-smooth. | |
| Nov 30, 2017 at 8:54 | comment | added | Nikolayevich | Thanks! I just found Pinelis' <Optimum bounds for the distributions of martingales in Banach spaces>, AOP 1994. Seems related. | |
| Nov 30, 2017 at 7:16 | comment | added | ofer zeitouni | By a result of Kallenberg and Sztencel (PTRF 1991), popularized recently by Lee and Peres, it is enough to reduce to $d=2$, where the result is true (maybe with 2 replaced by 4 in the denominator). The point is that the bound does not depend on the dimension. | |
| Nov 30, 2017 at 5:53 | history | asked | Nikolayevich | CC BY-SA 3.0 |