A note on central limit theorems for lattice models (Q1970852)

Let \(\{U_{ts}\}\), \(t=1,\dots,m_1\), \(s=1,\dots,m_2\), be a process defined on a two-dimensional lattice. Let \(m_1\), \(m_2\) be nonnegative integers. Assume that \(\{U_{ts}\}\) is stationary. The author defines that \(\{U_{ts}\}\) is \((m_1, m_2)\)-dependent if the sets \(\{U_{ij}, i\leq t, j\leq s\}\) and \(\{U_{ij}, i\geq t+m_1+1 \text{ or } j\geq s+m_2 +1\}\) are independent for each \((t,s)\). A central limit theorem (CLT) for \((m_1, m_2)\)-dependent processes is derived and generalized to a weighted CLT. Results of a simulation study are presented.