Abstract
We establish weak convergence rates for noise discretizations of a wide class of stochastic evolution equations with non-regularizing semigroups and additive or multiplicative noise. This class covers the nonlinear stochastic wave, HJMM, stochastic Schrödinger 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 essentially sharp.
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We are grateful to Arnulf Jentzen for pointing us to the topic and sharing with us ideas from unpublished joint work with Sonja Cox [5]. M. S. M. thankfully acknowledges support by the Swiss National Science Foundation through Grant SNF \(205121\_163425\). P. H. thankfully acknowledges support by the Freiburg Institute of Advanced Studies in the form of a Junior Fellowship.
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Harms, P., Müller, M.S. Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg–de Vries equations. Z. Angew. Math. Phys. 70, 16 (2019). https://doi.org/10.1007/s00033-018-1060-4
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DOI: https://doi.org/10.1007/s00033-018-1060-4