The Annals of Probability

Joint Continuity of Gaussian Local Times

Jack Cuzick and Johannes P. DuPreez

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Abstract

Sufficient conditions in terms of interpolation variances are given for a Gaussian process to have a jointly continuous local time. In the stationary case these conditions can be verified in terms of the spectral density and are seen to be within logarithmic factors of the best possible conditions. A bound for the modulus of continuity in the space variable is also obtained.

Article information

Source
Ann. Probab., Volume 10, Number 3 (1982), 810-817.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993789

Digital Object Identifier
doi:10.1214/aop/1176993789

Mathematical Reviews number (MathSciNet)
MR659550

Zentralblatt MATH identifier
0492.60032

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G17: Sample path properties 60G10: Stationary processes

Keywords
Occupation density local time Gaussian processes sample path continuity local nondeterminism

Citation

Cuzick, Jack; DuPreez, Johannes P. Joint Continuity of Gaussian Local Times. Ann. Probab. 10 (1982), no. 3, 810--817. doi:10.1214/aop/1176993789. https://projecteuclid.org/euclid.aop/1176993789


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