Exact Asymptotic Expression for the Density of Multiple Stochastic Integrals

We consider the exact asymptotic expression for the density of multiple stochastic integrals of the form
\begin{gather*} I-m(h)=\int_{X^m}h(x_1,x_2,\dots,x_m)\prod_{i=1}^mZ_G(dx_i), \end{gather*}
where $Z_G$ is the Gaussian orthogonal stochastic measure. In the two-dimensional case the result is general; for $m>2$, the kernel $h$ is required to satisfy the orthogonal symmetry condition.