  Based on the here developed functional analytic machinery we extend the
theory of operator sampling and identification to apply to operators with
stochastic spreading functions. We prove that identification with a delta train
signal is possible for a large class of stochastic operators that have the
property that the autocorrelation of the spreading function is supported on a
set of 4D volume less than one and this support set does not have a defective
structure. In fact, unlike in the case of deterministic operator
identification, the geometry of the support set has a significant impact on the
identifiability of the considered operator class. Also, we prove that,
analogous to the deterministic case, the restriction of the 4D volume of a
support set to be less or equal to one is necessary for identifiability of a
stochastic operator class.
