, Volume 84, Issue 3, pp 297-322

Stein's method for diffusion approximations

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.