The Annals of Probability

Local Holder Conditions for the Local Times of Certain Stationary Gaussian Processes

Laurie Davies

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Abstract

A local Holder condition is obtained for the local time of a stationary Gaussian process with spectral density function proportional to $(a^2 + \lambda^2)^{-(\alpha +\frac{1}{2})}$. A lower bound for the Hausdorff measure of the zero set of the process is also obtained.

Article information

Source
Ann. Probab., Volume 4, Number 2 (1976), 277-298.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996134

Digital Object Identifier
doi:10.1214/aop/1176996134

Mathematical Reviews number (MathSciNet)
MR423497

Zentralblatt MATH identifier
0331.60028

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G17: Sample path properties 60G25: Prediction theory [See also 62M20] 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Stationary Gaussian processes local time Holder conditions zero set Hausdorff measure

Citation

Davies, Laurie. Local Holder Conditions for the Local Times of Certain Stationary Gaussian Processes. Ann. Probab. 4 (1976), no. 2, 277--298. doi:10.1214/aop/1176996134. https://projecteuclid.org/euclid.aop/1176996134


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