On the joint distribution of ladder variables of random walk (Q1326326)
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scientific article; zbMATH DE number 569060
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the joint distribution of ladder variables of random walk |
scientific article; zbMATH DE number 569060 |
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On the joint distribution of ladder variables of random walk (English)
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14 July 1994
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The ladder time \(N\) and ladder height \(H\) of a random walk \(\{S_ n, n \geq 1\}\) as a pair \((N,H)\) lie in the domain of attraction of a bivariate stable law if \(S_ 1\) is in a domain of attraction, as was shown by \textit{P. E. Greenwood}, \textit{E. Omey} and \textit{J. L. Teugels} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 61, 527-539 (1982; Zbl 0493.60072)]. We prove a converse. If \(P(S_ n>0)\) converges and \((N,H)\) lies in a bivariate domain of attraction, then \(S_ 1\) is also in a domain of attraction.
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ladder time
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ladder height
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domain of attraction of a bivariate stable law
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