Stochastic evolution equations with random generators

Preprint enviat per a la seva publicació en una revista científica: The Annals of Probability, 1998, Vol. 26, No. 1, pp. 149–186. [http://doi.org/10.1214/aop/1022855415]We prove the existence of a unique mild solution for a stochastic evolution equation on a Hilbert space driven by a cylindrical Wiener process. The generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the Wiener process. The proof is based on a maximal inequality for the Skorohod integral deduced from the Itô’s formula for this anticipating stochastic integral