In this paper stochastic integrals with respect to the basic martingale are approximated by Gaussian processes. The probability inequalities governing this approximation are used to study goodness-of-fit tests based on sublinear functionals of weighted versions of these stochastic integrals. As special cases of these tests, generalized rank and supremum-type tests are considered.
"Approximation of Stochastic Integrals with Applications to Goodness-of-Fit Tests." Ann. Statist. 20 (1) 428 - 454, March, 1992. https://doi.org/10.1214/aos/1176348531