A functional central limit theorem for integrals of stationary mixing random fields

Jürgen Kampf; Evgeny Spodarev

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arXiv · 1512.03663

A functional central limit theorem for integrals of stationary mixing random fields

Jürgen Kampf·Evgeny Spodarev

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Abstract

We prove a functional central limit theorem for integrals $\int_W f(X(t))\, dt$, where $(X(t))_{t\in\mathbb{R}^d}$ is a stationary mixing random field and the stochastic process is indexed by the function $f$, as the integration domain $W$ grows in Van Hove-sense. We discuss properties of the covariance function of the asymptotic Gaussian process.

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Jürgen Kampf, Evgeny Spodarev. 2015-12-11. A functional central limit theorem for integrals of stationary mixing random fields. https://arxiv.org/abs/1512.03663

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