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Minimality, Rigidity, and Flows

  • Vladas Pipiras
  • Murad S. Taqqu
Chapter
Part of the SpringerBriefs in Probability and Mathematical Statistics book series (SBPMS )

Abstract

A symmetric stable random process has many integral representations. Among these, the so-called minimal representations play a fundamental role, as described in the chapter. Minimal representations are characterized by a rigidity property that allows relating stable processes with an invariance property to nonsingular flows and their functionals. Various types of nonsingular flows (dissipative, conservative, periodic, fixed and others) are also discussed. They underlie the decompositions of stable processes derived in the following chapter.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Vladas Pipiras
    • 1
  • Murad S. Taqqu
    • 2
  1. 1.Statistics and Operations ResearchUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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