  We prove that the mild solution to a semilinear stochastic evolution equation
on a Hilbert space, driven by either a square integrable martingale or a
Poisson random measure, is (jointly) continuous, in a suitable topology, with
respect to the initial datum and all coefficients. In particular, if the
leading linear operators are maximal (quasi-)monotone and converge in the
strong resolvent sense, the drift and diffusion coefficients are uniformly
Lipschitz continuous and converge pointwise, and the initial data converge,
then the solutions converge.
