WIAS Preprint No. 509, (1999)

The degrees of ill-posedness in stochastic and deterministic noise models


  • Nussbaum, Michael
  • Pereverzev, Sergei V.

2010 Mathematics Subject Classification

  • 62G05 65J10 41A25


  • Ill-posed problems, inverse estimation, operator equations, Gaussian noise, optimal difficulty, regularized inverse estimator


The degrees of ill-posedness for inverse estimation in Hilbert scales in the presence of deterministic and random noise are compared. For Gaussian random noise with different "smoothness" the optimal order of the rate of convergence for above mentioned estimation is indicated.

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