The Annals of Probability

Path Properties of Index-$\beta$ Stable Fields

John P. Nolan

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Abstract

We examine the paths of the stable fields that are the analogs of index-$\beta$ Gaussian fields. We find Holder conditions on their paths and find the Hausdorff dimension of the image, graph and level sets when we have local nondeterminism, generalizing the Gaussian results.

Article information

Source
Ann. Probab., Volume 16, Number 4 (1988), 1596-1607.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991586

Digital Object Identifier
doi:10.1214/aop/1176991586

Mathematical Reviews number (MathSciNet)
MR958205

Zentralblatt MATH identifier
0673.60043

JSTOR
links.jstor.org

Subjects
Primary: 60G17: Sample path properties
Secondary: 60G60: Random fields

Keywords
Stable processes random fields Hausdorff dimension local times local nondeterminism

Citation

Nolan, John P. Path Properties of Index-$\beta$ Stable Fields. Ann. Probab. 16 (1988), no. 4, 1596--1607. doi:10.1214/aop/1176991586. https://projecteuclid.org/euclid.aop/1176991586


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Corrections

  • See Correction: John P. Nolan. Correction: Path Properties of Index-$\beta$ Stable Fields. Ann. Probab., Volume 20, Number 3 (1992), 1601--1602.