Stable-bounded subsets of Lα, and sample unboundedness of symmetric stable processes

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Abstract

Let Xt be the Levy symmetric stable process with index α ∈ [1, 2), and let C be a convex, symmetric subset of Lα[0, 1]. We prove that if C does not have compact closure then supf{hook}ε{lunate}C |∝01f{hook}(t)dXt| is infinite with probability one. This extends a result of Dudley in the case α = 2.

Original languageEnglish (US)
Pages (from-to)265-279
Number of pages15
JournalJournal of Functional Analysis
Volume60
Issue number2
DOIs
StatePublished - Feb 1 1985
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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