The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \&R\"ockner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appearin the Trans.\ Amer.\ Math.\ Soc.] has turned out to be a useful instrument tostudy solutions and numerical approximations of stochastic partial differentialequations (SPDEs) which are formulated as stochastic evolution equations (SEEs)on Hilbert spaces. In this article we generalize this mild It\^o formula sothat it is applicable to solutions and numerical approximations of SPDEs whichare formulated as SEEs on UMD (unconditional martingale differences) Banachspaces. This generalization is especially useful for proving essentially sharpweak convergence rates for numerical approximations of SPDEs.
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