A note on conjugate \(\Pi\)-variation and a weak limit theorem for the number of renewals (Q1095507)
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scientific article; zbMATH DE number 4028570
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on conjugate \(\Pi\)-variation and a weak limit theorem for the number of renewals |
scientific article; zbMATH DE number 4028570 |
Statements
A note on conjugate \(\Pi\)-variation and a weak limit theorem for the number of renewals (English)
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1988
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Let \(X_ 1,X_ 2,..\). be i.i.d. and positive random variables and put \[ N(t)=\max \{k: X_ 1+...+X_ k\leq t\}. \] If the tails of \(X_ i\) are regularly varying with index -1 then it is known that N(t), suitably normalized, tends in distribution to a stable law of order 1 as \(t\to \infty\). The authors give an alternative expression for the normalizing functions and discuss related conjugation concepts.
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renewal theory
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regular variation
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conjugation concepts
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