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Compound Poisson approximation for unbounded functions on a group, with application to large deviations
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  • Published: December 1995

Compound Poisson approximation for unbounded functions on a group, with application to large deviations

  • L. H. Y. Chen1 &
  • M. Roos2 

Probability Theory and Related Fields volume 103, pages 515–528 (1995)Cite this article

  • 87 Accesses

  • 13 Citations

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Summary

A second order error bound is obtained for approximating ∫h d \(\tilde Q\) by ∫h d \(\tilde Q\), where\(\tilde Q\) is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to\({{d\tilde Q} \mathord{\left/ {\vphantom {{d\tilde Q} {dQ}}} \right. \kern-\nulldelimiterspace} {dQ}}\). The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, 0511, Singapore, Republic of Singapore

    L. H. Y. Chen

  2. Abteilung Biostatistik, ISPm, Universität Zürich, Sumatrastrasse 30, CH-8006, Zürich, Switzerland

    M. Roos

Authors
  1. L. H. Y. Chen
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  2. M. Roos
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Additional information

Research of the second author was supported by Schweizerischer Nationalfonds

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Cite this article

Chen, L.H.Y., Roos, M. Compound Poisson approximation for unbounded functions on a group, with application to large deviations. Probab. Th. Rel. Fields 103, 515–528 (1995). https://doi.org/10.1007/BF01246337

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  • Received: 24 October 1994

  • Revised: 24 May 1995

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01246337

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Mathematics Subject Classification

  • 60B10
  • 60F05
  • 60F10
  • 60B15
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