High excursion probabilities for Gaussian fields on smooth manifolds

Vladimir I. Piterbarg

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arXiv · 2108.07473

High excursion probabilities for Gaussian fields on smooth manifolds

Vladimir I. Piterbarg

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Abstract

Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large excursion probabilities have been evaluated. Vector Gaussian processes, chi-square processes, Bessel process, fractional Bessel process, Bessel bridge are examples of application of this result.

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Vladimir I. Piterbarg. 2021-08-17. High excursion probabilities for Gaussian fields on smooth manifolds. https://arxiv.org/abs/2108.07473

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