Lévy processes and Lévy white noise as tempered distributions

• Robert C. Dalang ^[1] ; Thomas Humeau ^[1]
  1. [1] Swiss Federal Institute of Technology in Zurich

     Swiss Federal Institute of Technology in Zurich

     Zürich, Suiza

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 2, 2017, págs. 4389-4418
• Idioma: inglés
• DOI: 10.1214/16-AOP1168
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• Resumen

  • We identify a necessary and sufficient condition for a Lévy white noise to be a tempered distribution. More precisely, we show that if the Lévy measure associated with this noise has a positive absolute moment, then the Lévy white noise almost surely takes values in the space of tempered distributions. If the Lévy measure does not have a positive absolute moment of any order, then the event on which the Lévy white noise is a tempered distribution has probability zero.