Approximating multiple itô integrals with "band limited" processes

Abstract

Let denote a "wide-band width" vector valued process. The paper is concerned with limits of , and for the ra-multiple integral case. For the most important case, a weak convergence result is obtained, and the "correction'" terms exhibited. The method is such that the conditions used can readily be weakened. An application to a likelihood functional and hypothesis testing problem is given. There, the weak convergence result (rather than mere convergence of finite dimensional distributions) is essential if the limit approximation is to make sense as an approximation to the likelihood functional. The correction terms depend only on the limit (as a-0) of the correlation function of the(renormalized)