On the strong (C, α) laws of large numbers
We give a necessary and sufficient condition for the strong (C, α) law of large numbers with real order α > 0 for weighted sums of independent random variables satisfying the property α-WH analogous to, though weaker than, the Hartman’s type property. In particular, if a sequence of random variab...
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| Main Author: | |
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| Format: | Article |
| Published: |
2021
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| Series: | Acta scientiarum mathematicarum
87 No. 3-4 |
| Kulcsszavak: | Valószínűségszámítás, Matematika |
| Subjects: | |
| doi: | 10.14232/actasm-021-271-y |
| Online Access: | http://acta.bibl.u-szeged.hu/75860 |
| Summary: | We give a necessary and sufficient condition for the strong (C, α) law of large numbers with real order α > 0 for weighted sums of independent random variables satisfying the property α-WH analogous to, though weaker than, the Hartman’s type property. In particular, if a sequence of random variables is two-sided, then the strong (C, α) law of large numbers for the sequence can also be characterized by the ergodic Hilbert transform. |
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| Physical Description: | 679-707 |
| ISSN: | 2064-8316 |