  This article presents a coupling approach for the approximation of iterated
stochastic integrals of length three. The generation of such integrals is the
central problem of higher-order pathwise approximations for SDEs, which still
lacks a satisfactory answer due to the restriction of dimensionality and
computational load. Here we start from the Fourier representation of the triple
stochastic integral and investigate the global behaviour of the joint density
of the representation. Finally in the main result we give a coupling in the
quadratic Vaserstein distance.
