Approximation and convergence of solutions to semilinear stochastic   evolution equations with jumps
  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. 
Carlo Marinelli, Luca Di Persio, Giacomo Ziglio
math.AP math.PR