Large deviation probabilities for random walks with heavy tails (Q1876391)
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scientific article; zbMATH DE number 2097083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Large deviation probabilities for random walks with heavy tails |
scientific article; zbMATH DE number 2097083 |
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Large deviation probabilities for random walks with heavy tails (English)
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6 September 2004
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The authors consider the sums and maxima of sequential sums of random variables with regularly varying distribution tails of index \(-\beta\), with \(\beta\in (1,2)\). First-order approximations are established as well as some refinements for the distributions of these sums and maxima in a large deviation area. Similar results are obtained for probabilities of crossing arbitrary curvilinear boundaries in the large deviation range by random walks generated by such sequential sums.
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regularly varying distribution tail
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refinement of large deviation probabilities
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asymptotic expansion
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boundary crossing probability
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