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1982•The Annals of ProbabilityOpen access

Joint Continuity of Gaussian Local Times

Jack M. Cuzick, 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.

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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.

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Available 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.

Key concepts: Mathematics, Modulus of continuity, Gaussian process, Logarithm, Gaussian, Interpolation (computer graphics), Mathematical analysis, Gaussian random field

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