On the supremum of an infinitely divisible process

Willekens, Eric

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Publication date

December 1987

DOI

10.1016/0304-4149(87)90058-5

Publisher

Published by Elsevier B.V.

ISSN

0304-4149

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Abstract

AbstractIt was shown by Berman in a recent paper that, for any infinitely divisible process X = {Xt, t⩾0} with symmetric increments, P(sup0⩽s⩽t Xs⩾u) ∼ P(Xt⩾u) (u → ∞) if the right tail of the Lévy measure is regularly varying with index 0<α<2. In this note we use a simple argument to show that this result is true for a more general class of processes

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On the supremum of an infinitely divisible process

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On the supremum of an infinitely divisible process

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