Probability Theory and Related Fields

, Volume 84, Issue 3, pp 297–322

Stein's method for diffusion approximations

  • A. D. Barbour

DOI: 10.1007/BF01197887

Cite this article as:
Barbour, A.D. Probab. Th. Rel. Fields (1990) 84: 297. doi:10.1007/BF01197887


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.

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

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