On the construction and limit behaviour of a multiple stochastic integral for the diffusion process

We give the definition of the multiple integral
$$ I_f=\int_0^T\dotsi\int_0^Tf(\xi(t_1),\dots,\xi(t_m))\,d\xi(t_1)\dots d\xi(t_m) $$
where $\xi(t)$ is the solution of the Ito's diffusion equation
$$ d\xi(t)=a(t,\xi(t))\,dt+\sigma(t,\xi(t))\,dw(t). $$
The asymptotic distributions of the integral $I_t$ are investigated.