A stochastic measure and nonlinear approximation of some random fields

For a random field $\{H_p(x,y),x,y\ge0\}$ where $H_p(x,y)=H_p(\eta(x,y))$, $H_p(z)$ is the Hermite polynomial of degree $p$ and $\{\eta(x,y),x,y\ge0\}$ is a real Gaussian random field with $\eta(0,y)=\eta(x,0)=\mathbf{E}\eta(x,y)=0$ a stochastic measure and nonlinear approximations are introduced and properties of mean-square error of approximations are studied.