Probability Theory and Related Fields

, Volume 84, Issue 3, pp 297–322 | Cite as

Stein's method for diffusion approximations

  • A. D. Barbour
Article

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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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. D. Barbour
    • 1
  1. 1.Institut für Angewandte MathematikUniversität ZürichZürichSwitzerland

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