A two-parameter maximal ergodic theorem with dependence (Q1109913)
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scientific article; zbMATH DE number 4071266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A two-parameter maximal ergodic theorem with dependence |
scientific article; zbMATH DE number 4071266 |
Statements
A two-parameter maximal ergodic theorem with dependence (English)
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1987
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Let \(X_ 1,X_ 2,..\). and \(Y_ 1,Y_ 2,..\). be independent sequences of i.i.d. U(0,1) random variables. We characterize completely those Borel functions F on \([0,1]^ 2\) for which the strong law of large numbers and the maximal ergodic theorem hold for the doubly indexed family \((1/nm)\sum_{i\leq n,j\leq m}F(X_ i,Y_ j).\)
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two-parameter martingales
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decoupling
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strong law of large numbers
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maximal ergodic theorem
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