Stochastic Bounds for Lévy Processes
Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy proces...
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| Veröffentlicht in: | The Annals of probability 2004-04, Vol.32 (2), p.1545-1552 |
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| container_title | The Annals of probability |
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| creator | Doney, R. A. |
| description | Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Lévy processes which converge to ∞ in probability. |
| doi_str_mv | 10.1214/009117904000000315 |
| format | Article |
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A.</creatorcontrib><title>Stochastic Bounds for Lévy Processes</title><title>The Annals of probability</title><description>Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. 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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | 60G17 60G51 Determinism Exact sciences and technology exit times Infinity Mathematical analysis Mathematics Probability Probability and statistics Probability theory and stochastic processes Processes with independent increments Random variables Random walk random walks Sciences and techniques of general use Stochastic processes Studies weak drift to infinity |
| title | Stochastic Bounds for Lévy Processes |
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