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Stein's method for diffusion approximations
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  • Published: September 1990

Stein's method for diffusion approximations

  • A. D. Barbour1 

Probability Theory and Related Fields volume 84, pages 297–322 (1990)Cite this article

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Summary

Stein's method of obtaining distributional approximations is developed in the context of functional approximation by the Wiener process and other Gaussian processes. An appropriate analogue of the one-dimensional Stein equation is derived, and the necessary properties of its solutions are established. The method is applied to the partial sums of stationary sequences and of dissociated arrays, to a process version of the Wald-Wolfowitz theorem and to the empirical distribution function.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Zürich, Rämistrasse 74, CH-8001, Zürich, Switzerland

    A. D. Barbour

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  1. A. D. Barbour
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Barbour, A.D. Stein's method for diffusion approximations. Probab. Th. Rel. Fields 84, 297–322 (1990). https://doi.org/10.1007/BF01197887

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  • Received: 11 October 1988

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01197887

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Keywords

  • Distribution Function
  • Stochastic Process
  • Stein
  • Probability Theory
  • Mathematical Biology
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