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We establish weak convergence rates for noise discretizations of a wide classof stochastic evolution equations with non-regularizing semigroups and additiveor multiplicative noise. This class covers the nonlinear stochastic wave, HJMM,stochastic Schr\"odinger and linearized stochastic Korteweg-de Vries equation.For several important equations, including the stochastic wave equation,previous methods give only suboptimal rates, whereas our rates are essentiallysharp.

zeitschrift für angewandte mathematik und physik

Weak convergence rates for stochastic evolution equations and  applications to nonlinear stochastic wave, HJMM, stochastic Schr\"odinger and  linearized stochastic Korteweg-de Vries equations