Stein's method for diffusion approximations
- Cite this article as:
- Barbour, A.D. Probab. Th. Rel. Fields (1990) 84: 297. doi:10.1007/BF01197887
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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.