  Employing recent results on stochastic differential equations associated with
the standard model of non-relativistic quantum electrodynamics by B. G\"uneysu,
J.S. M{\o}ller, and the present author, we study the continuity of the
corresponding semi-group between weighted vector-valued L^p-spaces, continuity
properties of elements in the range of the semi-group, and the pointwise
continuity of an operator-valued semi-group kernel. We further discuss the
continuous dependence of the semi-group and its integral kernel on model
parameters. All these results are obtained for Kato decomposable electrostatic
potentials and the actual assumptions on the model are general enough to cover
the Nelson model as well. As a corollary we obtain some new pointwise
exponential decay and continuity results on elements of low-energetic spectral
subspaces of atoms or molecules that also take spin into account. In a simpler
situation where spin is neglected we explain how to verify the joint continuity
of positive ground state eigenvectors with respect to spatial coordinates and
model parameters. There are no smallness assumptions imposed on any model
parameter.
