Moment inequality for the martingale square function (Q2866790)
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scientific article; zbMATH DE number 6238615
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Moment inequality for the martingale square function |
scientific article; zbMATH DE number 6238615 |
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16 December 2013
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martingales
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sum of squares of the increments
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method of moments
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best constants
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Moment inequality for the martingale square function (English)
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Consider a martingale sequence over a filtration. The main result of this work provides an upper bound on the first moment of the \(n\)th term of the sequence by the sum of the squares of the increments of the sequence up to the \(n\)th term. This upper bound carries a multiplicative factor which is a function of \(n\) and it is determined explicitly through a recursion. This multiplicative factor is best possible in the sense that there is a martingale sequence that almost attains it.
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0.8340504765510559
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0.8323380351066589
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0.8143806457519531
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