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On a family of Lévy processes without support in S′

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  • Mendes, R. Vilela

Abstract

The distributional support of the sample paths of Lévy processes is an important issue for the construction of sparse statistical models, theories of integration in infinite dimensions and the existence of generalized solutions of stochastic partial differential equations driven by Lévy white noise. Here one considers a family Kα0<α<2 of Lévy processes which are a. s. not supported in S′. For 1<α<2 they are supported in K′, the space of distributions of exponential type and for 0<α≤1 on generalized spaces of power exponential type.

Suggested Citation

  • Mendes, R. Vilela, 2024. "On a family of Lévy processes without support in S′," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715224000464
    DOI: 10.1016/j.spl.2024.110077
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    References listed on IDEAS

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    1. Fageot, Julien & Humeau, Thomas, 2021. "The domain of definition of the Lévy white noise," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 75-102.
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