The supremum of a process with stationary independent and symmetric increments

Let Xt, t [greater-or-equal, slanted] 0, be a process with stationary independent and symmetric increments. If the tail of the Lévy spectral measure in the representation of the characteristic function is of regular variation of index -[alpha], for some 0 < [alpha] < 2, then Pp(Xs: 0[less-than-or-equals, slant]s[less-than-or-equals, slant]t) > u) ~ P(Xt, > u), for u --> [infinity],for each t > 0.

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Year of publication:	1986
Authors:	Berman, Simeon M.
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 23.1986, 2, p. 281-290
Publisher:	Elsevier
Keywords:	Independent increments * supremum distribution * regular variation * sojourn above high level

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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