This article is cited in 3 papers

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

J. Kampf, E. Spodarev

Institute of Stochastics, Ulm University, Germany

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

Keywords: functional central limit theorem, $\mathrm{GB}$-set, Meixner system, mixing, random field.

Received: 17.03.2016
Revised: 17.05.2017
Accepted: 22.05.2017

Language: English

DOI: 10.4213/tvp5161

 English version: Theory of Probability and its Applications, 2018, 63:1, 135–150

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