  Skew convolution semigroups play an important role in the study of
generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a
characterization for a general skew convolution semigroup on real separable
Hilbert space whose characteristic functional is not necessarily differentiable
at the initial time. A connection between this subject and catalytic branching
superprocesses is established through fluctuation limits, providing a rich
class of non-differentiable skew convolution semigroups. Path regularity of the
corresponding generalized Ornstein-Uhlenbeck processes in different topologies
is also discussed.
