A central limit theorem for stationary random fields

Details A central limit theorem for stationary random fields A central limit theorem for stationary random fields

2011-09-05

arxiv.org/abs/1109.0838v1

Mathematics

Probability

21 pages

Scientific paper

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k = g(epsilon_{k-s}, s \in \Z^d)$, $k\in\Z^d$, where $(\epsilon_i)_{i\in\Z^d}$ are i.i.d random variables and $g$ is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established.

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