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Bounded Stationary Stable Processes and Entropy

  • John P. Nolan
Part of the Progress in Probabilty book series (PRPR, volume 25)

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.

Keywords

Sample Path Stable Process Stationary Increment Finite Dimensional Distribution Symmetric Stable Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Nolan, J. P. “Continuity of symmetric stable processes.” J. Multivar. Analysis 29, 84–93 (1989).MathSciNetMATHCrossRefGoogle Scholar
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    Talagrand, M. “Necessary conditions for sample boundedness of p-stable processes.” Annals of Probability 16, 1584–1595 (1988).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • John P. Nolan
    • 1
  1. 1.Department of Mathematics and StatisticsAmerican UniversityUSA

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