A central limit theorem for stationary random fields

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 $X_k = g(\varepsilon_{k-s}, s \in \Z^d)$, $k\in\Z^d$, where $(\varepsilon_i)_{i\in\Z^d}$ 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.Comment: 22 page

On Beveridge-Nelson decomposition and limit theorems for linear random fields

We consider linear random fields and show how an analogue of the Beveridge-Nelson decomposition can be applied to prove limit theorems for sums of such fields.Limit theorems Random fields