  The intrinsic volumes induced by a stationary Poisson k-flat process inside a
compact and convex sampling window are considered. Using techniques from
stochastic analysis, more precisely calculus with multiple stochastic integrals
and a Wiener-Ito chaos expansion of Poisson functionals, all moments and
cumulants, exact and asymptotic, are calculated in terms of a family of
integral-geometric functionals. Moreover, univariate central limit theorems as
well as Berry-Esseen-type inequalities are shown and a multidimensional limit
theorem is concluded.
