Lower Bounds and Non-Uniform Time Discretization for Approximation of Stochastic Heat Equations

@article{Ritter2004LowerBA,
  title={Lower Bounds and Non-Uniform Time Discretization for Approximation of Stochastic Heat Equations},
  author={Klaus Ritter and Thomas M{\"u}ller-Gronbach},
  journal={Foundations of Computational Mathematics},
  year={2004},
  volume={7},
  pages={135-181}
}
We study algorithms for approximation of the mild solution of stochastic heat equations on the spatial domain ]0, 1[. The error of an algorithm is defined in L2-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… CONTINUE READING

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