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On the First Exit Time of a Completely Asymmetric Stable Process from a Finite Interval
Author(s) -
Bertoin Jean
Publication year - 1996
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/28.5.514
Subject(s) - mathematics , interval (graph theory) , law of the iterated logarithm , laplace transform , extension (predicate logic) , iterated function , logarithm , distribution (mathematics) , iterated logarithm , mathematical analysis , pure mathematics , combinatorics , computer science , programming language
We compute the Laplace transform of the distribution of the first exit time from a finite interval for a completely asymmetric stable process. The formula involves a Mittag‐Leffler function and its derivative. As an application, we determine the asymptotic tail behaviour of the foregoing distribution, and deduce an extension of the law of the iterated logarithm of Chung.