Regularized Inversion of Noisy Laplace Transforms

Regularized Inversion of Noisy Laplace Transforms

In this paper we construct a sequence of regularized inverses of the Laplace transform by relating this transform to a convolution operator for functions on the group of the positive real numbers with multiplication. Estimation of the mixing distribution, when a mixture of exponential distributions...

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Veröffentlicht in:Advances in applied mathematics 1994-06, Vol.15 (2), p.186-201
Hauptverfasser: Chauveau, D.E., Vanrooij, A.C.M., Ruymgaart, F.H.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Integral transforms, operational calculus
Mathematical analysis
Mathematics
Sciences and techniques of general use
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Beschreibung
Zusammenfassung:In this paper we construct a sequence of regularized inverses of the Laplace transform by relating this transform to a convolution operator for functions on the group of the positive real numbers with multiplication. Estimation of the mixing distribution, when a mixture of exponential distributions is observed, is an example. Inversion of perturbed Laplace transforms also plays a role in system theory.
ISSN:0196-8858
1090-2074
DOI:10.1006/aama.1994.1007