'Poisson-Voronoi approximation and Wiener-Ito-chaos expansions'

Let $X$ be a Poisson point process and $K$ a d-dimensional convex set.
For a point $x \in X$ denote by $v_X(x)$ the Voronoi cell with respect to $X$, and set $$ v_X (K) := \bigcup_{x \in X \cap K } v_X(x) $$ which is the union of all Voronoi cells with center in $K$. We call $v_X(K)$ the Poisson-Voronoi approximation of $K$.
For $K$ a compact convex set the volume difference $V_d(v_X(K))-V_d(K) $ and the symmetric difference $V_d(v_X(K) \triangle K)$ are investigated.
Estimates for the variance and limit theorems are obtained using the chaotic decomposition of these functions in multiple Wiener-Ito integrals