LEVY PROCESSES AND LEVY WHITE NOISE AS TEMPERED DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Dalang, Robert C.; Humeau, Thomas
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1168
• 发表日期: 2017
• 页码: 4389-4418
• 关键词: sharp markov property

摘要

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