| Contents |
| We consider an abstract time-delayed stochastic evolution equation in an infinite dimensional separable Hilbert space driven by additive or multiplicative L\'evy noise. The setting can handle both finite and infinite delay. Furthermore we include Lipschitz nonlinearities. We present a transformation approach, which transforms the original problem into a classic stochastic abstract Cauchy problem. We show the equivalence of mild solutions for the two problems. Since the solution neither has stochastic differentials nor need to be c\`adl\`ag we present approximations, where each member of the approximating sequence has those properties. Finally we give an outlook how these approximations can be used to handle problems involving stochastic delay equations. |
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