## The Annals of Probability

### Path Properties of Index-$\beta$ Stable Fields

John P. Nolan

#### 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

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