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Stochastic regularization of linear equations and the realization of Gaussian fields

Author

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  • Piccioni, Mauro
  • Roma, Massimo

Abstract

The variational representation of the conditional expectation of a Gaussian signal X given observations Y corrupted by independent white noise is investigated in the general infinite-dimensional setting. Under Hilbert-Schmidt type assumptions it is shown that the filter can be realized on sample configurations Y[omega] as the extension by continuity of the mapping that gives the solution of a related variational problem.

Suggested Citation

  • Piccioni, Mauro & Roma, Massimo, 1990. "Stochastic regularization of linear equations and the realization of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 143-150, April.
    • Handle: RePEc:eee:jmvana:v:33:y:1990:i:1:p:143-150
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