An almost sure functional limit theorem at zero for a class of Levy processes normed by the square root function, and applications

Buchmann, Boris; Maller, Ross; Szimayer, Alex

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An almost sure functional limit theorem at zero for a class of Levy processes normed by the square root function, and applications

Date

2008

Authors

Buchmann, Boris

Maller, Ross

Szimayer, Alex

Publisher

Springer

Abstract

A recent result of Bertoin, Doney and Maller (Ann. Prob., 2007) gives an integral condition to characterize the class of Lévy processes X(t) for which lim supt↓0 |X (t)|/√t ∈ (0, ∞) occurs almost surely (a.s.). For such processes we have a kind o