A stochastic measure and nonlinear approximation of some random fields

For a random field $\{ H_p (x,y), x,y \geqq 0\} $ 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 \geqq 0\} $ is a real Gaussian random field with $\eta (0,y) = \eta (x,0) = {\bf E} \eta (x,y) = 0$ a stochastic measure and nonlinear approximations are introduced and properties of mean-square error of approximations are studied.