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Rates of uniform convergence in the real inversion theorem for Laplace transforms

Published online by Cambridge University Press:  01 January 1999

JOSÉ A. ADELL  and
CARMEN SANGÜESA
JOSÉ A. ADELL
Affiliation:
Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza. 50009 Zaragoza (Spain). e-mail: adell@posta.unizar.es
CARMEN SANGÜESA
Affiliation:
Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza. 50009 Zaragoza (Spain)
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Abstract

We obtain sharp rates of uniform convergence in the real inversion theorem for Laplace transforms. This entails giving estimates of the Kolmogorov distance between normalized Poisson mixtures and their mixing distribution. Our approach combines probabilistic representations in terms of gamma processes with approximation-theoretic techniques.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 125 , Issue 1 , January 1999 , pp. 139 - 149
Copyright
Cambridge Philosophical Society 1999

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Footnotes

Research supported by the Grant PB92-0437 of the Spanish DGICYT.