## The Annals of Probability

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

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

#### 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