The Simulation of a Class of Random Fields

A random field $\xi_x(\omega)(\mathbf{x}\in T^2)$ where $T^2$ is the two-dimension lattice, is called weakly dependent if, for every $\mathbf{x}=(x_1,x_2)\in T^2$, the random variable $\xi_x(\omega)$ depends only on the random variables $\xi_y(\omega)$ at points $\mathbf{y}=(x_1-1, x_2)$, $(x_1+1, x_2)$, $(x_1, x_2-1)$, $(x_1, x_2+1)$.
In this paper, a method of simulation of weakly dependent Gaussian random fields is proposed.