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

Terry R. McConnell

doi:10.1016/0022-1236(85)90053-9

Stable-bounded subsets of L^α, and sample unboundedness of symmetric stable processes

Terry R. McConnell

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	265-279
Number of pages	15
Journal	Journal of Functional Analysis
Volume	60
Issue number	2
DOIs	https://doi.org/10.1016/0022-1236(85)90053-9
State	Published - Feb 1 1985
Externally published	Yes

ASJC Scopus subject areas

Analysis

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10.1016/0022-1236(85)90053-9

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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.",

author = "McConnell, {Terry R.}",

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N2 - 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.

AB - 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.

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Stable-bounded subsets of L^α, and sample unboundedness of symmetric stable processes

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