The Annals of Probability

Continuity of Gaussian Local Times

Jack Cuzick

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Abstract

Continuity in the time parameter is considered for a natural version of the local time for stationary Gaussian processes. Bounds are given for the local and uniform modulus of continuity which are applicable in cases not covered by Kono, notably when the incremental variance is a regularly varying function of index two.

Article information

Source
Ann. Probab., Volume 10, Number 3 (1982), 818-823.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993790

Digital Object Identifier
doi:10.1214/aop/1176993790

Mathematical Reviews number (MathSciNet)
MR659551

Zentralblatt MATH identifier
0492.60033

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G17: Sample path properties 60G10: Stationary processes 60G25: Prediction theory [See also 62M20]

Keywords
Local time Gaussian processes sample continuity nondeterminism

Citation

Cuzick, Jack. Continuity of Gaussian Local Times. Ann. Probab. 10 (1982), no. 3, 818--823. doi:10.1214/aop/1176993790. https://projecteuclid.org/euclid.aop/1176993790


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