WIAS Preprint No. 370, (1997)

Statistical approach to inverse boundary problems for partial differential equations



Authors

  • Golubev, Georgi
  • Khasminskii, Rafail

2010 Mathematics Subject Classification

  • 62G05

Keywords

  • Partial differential equation, minimax estimator, boundary problem

Abstract

Inverse problems for elliptic and parabolic partial differential equations are considered. It is assumed that a solution of the equation is observed in white Gaussian noise with a small spectral density. The goal is to recover smooth but unknown boundary or initial conditions based on the noisy data. It is shown that the second order minimax estimators are linear as the spectral density of the noise goes to zero.

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