Extremes of locally stationary Gaussian and chi fields on manifolds

Wanli Qiao

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arXiv · 2005.07185

Extremes of locally stationary Gaussian and chi fields on manifolds

Wanli Qiao

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Abstract

Depending on a parameter $h\in (0,1]$, let $\{X_h(\mathbf{t})$, $\mathbf{t}\in\mathcal{M}_h\}$ be a class of centered Gaussian fields indexed by compact manifolds $\mathcal{M}_h$. For locally stationary Gaussian fields $X_h$, we study the asymptotic excursion probabilities of $X_h$ on $\mathcal{M}_h$. Two cases are considered: (i) $h$ is fixed and (ii) $h\rightarrow0$. These results are extended to obtain the limit behaviors of the extremes of locally stationary $\chi$-fields on manifolds.

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Wanli Qiao. 2020-05-14. Extremes of locally stationary Gaussian and chi fields on manifolds. https://arxiv.org/abs/2005.07185

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