Average Case Complexity of Weighted Approximation and Integration over R+

@article{Plaskota2002AverageCC,
  title={Average Case Complexity of Weighted Approximation and Integration over R+},
  author={Leszek Plaskota and Klaus Ritter and Grzegorz W. Wasilkowski},
  journal={J. Complexity},
  year={2002},
  volume={18},
  pages={517-544}
}
We study weighted approximation and integration of Gaussian stochastic processes X deened over R + whose rth derivatives satisfy a HH older condition with exponent in the quadratic mean. We assume that the algorithms use samples of X at a nite number of points. We study the average case (information) complexity, i.e., the minimal number of samples that are suucient to approximate/integrate X with the expected error not exceeding ". We provide suucient conditions in terms of the weight and the… CONTINUE READING

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