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Lower Bounds and Non-Uniform Time Discretization for Approximation of Stochastic Heat Equations Ritter, Klaus Müller-Gronbach, Thomas Stochastic heat equation Non-uniform time discretization minimal errors upper and lower bounds We study algorithms for approximation of the mild solution of stochastic heat equations on the spatial domain ]0,1[^d. The error of an algorithm is defined in L_2-sense. We derive lower bounds for the error of every algorithm that uses a total of N evaluations of one-dimensional components of the driving Wiener process W. For equations with additive noise we derive matching upper bounds and we construct asymptotically optimal algorithms. The error bounds depend on N and d, and on the decay of eigenvalues of the covariance of W in the case of nuclear noise. In the latter case the use of non-uniform time discretizations is crucial. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Klaus Ritter and Thomas Müller-Gronbach 2005 Is Part Of Dagstuhl Seminar Proceedings, Volume 4401, Algorithms and Complexity for Continuous Problems (2005) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.04401.6 urn:nbn:de:0030-drops-1518 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04401.6 eng https://creativecommons.org/licenses/by/4.0/legalcode