Bounded Stationary Stable Processes and Entropy

Nolan, John P.

doi:10.1007/978-1-4684-6778-9_5

John P. Nolan⁴

Part of the book series: Progress in Probabilty ((PRPR,volume 25))

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Abstract

In this paper we will show that any stationary or stationary increment p-stable process, 1≤p<2, that is sample bounded has a finite metric entropy integral. The result is an application of Talagrand’s work on majorizing measures for stable processes [7]. We combine this result with earlier results to give necessary conditions for a stationary increment stable process to have a.s. bounded or a.s. continuous sample paths.

We show that a bounded stationary stable process has a finite metric entropy integral. Necessary conditions for sample boundedness and sample path continuity are given.

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References

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Authors and Affiliations

Department of Mathematics and Statistics, American University, Washington, DC, USA
John P. Nolan

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John P. Nolan
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Editors and Affiliations

Department of Statistics, University of North Carolina, Chapel Hill, NC, 27599, USA
Stamatis Cambanis
Engineering Theory Center, Cornell University, Ithaca, NY, 14853, USA
Gennady Samorodnitsky
Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA, 02215, USA
Murad S. Taqqu

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Nolan, J.P. (1991). Bounded Stationary Stable Processes and Entropy. In: Cambanis, S., Samorodnitsky, G., Taqqu, M.S. (eds) Stable Processes and Related Topics. Progress in Probabilty, vol 25. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6778-9_5

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DOI: https://doi.org/10.1007/978-1-4684-6778-9_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-6780-2
Online ISBN: 978-1-4684-6778-9
eBook Packages: Springer Book Archive

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