Small-time moment asymptotics for Lévy processes

José E. Figueroa-López

Statistics & Probability Letters, 2008, vol. 78, issue 18, 3355-3365

Abstract: Conditions ensuring that are given for a Lévy process X with Lévy measure [nu] and for unbounded moment functions f. Compared with previous works, the moment functions considered here satisfy very mild conditions aimed at controlling how fast f grows at infinity. As an application of our results, the infinitesimal generator of the Lévy process is shown to be well-defined in a class of smooth unbounded functions equipped with a suitable norm. Also, the rate of convergence is studied when f is a smooth function vanishing in a neighborhood of the origin.

Date: 2008
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