Abstract
A class of stochastic delay equations in a type 2 umd Banach space E driven by the cylindrical Wiener process is studied. We investigate two concepts of solutions: weak and generalised strong, and give conditions under which they are equivalent. We present an evolution equation approach in a Banach space Ep:=E×Lp(−1,0;E) proving that the solutions can be reformulated as Ep-valued Markov processes. Based on the Markovian representation we prove the existence and continuity of the solutions. The results are applied to stochastic reaction–diffusion equations with delays.
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