Probability Theory and Related Fields

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

Stein's method for diffusion approximations

  • A. D. Barbour


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.


Distribution Function Stochastic Process Stein Probability Theory Mathematical Biology 
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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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