Existence and regularization of the local times of a Gaussian process

Abstract

We study an existence result in the mean square sense of the local times of a one-dimensional Gaussian process defined by an indefinite Wiener integral. For any spatial dimension, we prove that the local times of a Gaussian process, after appropriatelly renormalized, exist as White noise distributions. We also present a regularization of the local times and show a convergence result in Hida distributions space.

Keywords

• Local times,b-Gaussian process,white noise analysis.

References

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