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The Segal-Bargmann transform for Lévy white noise functionals associated with non-integrable Lévy processes. (English) Zbl 1147.60047

Summary: By using a method of truncation, we derive the closed form of the Segal-Bargmann transform of Lévy white noise functionals associated with a Lévy process with the Lévy spectrum without the moment condition. Besides, a sufficient and necessary condition to the existence of Lévy stochastic integrals is obtained.

MSC:

60H40 White noise theory
60G51 Processes with independent increments; Lévy processes
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