The central limit theorem for stochastic integrals (Q1081181)

The central limit theorem for \({\mathcal D}[0,1]^ q\)-valued random variables of the form \(\int^{t}_{0}f(s,\omega)M(ds,\omega)\) is proved, where f(s,\(\omega)\) is a process over \([0,1]^ q\) and M is a certain random measure. This is an extension of the corresponding result for \(q=1\) by \textit{E. Giné} and \textit{M. B. Marcus} [Ann. Prob. 11, 58-77 (1983; Zbl 0504.60011)]. To prove this, some results on the tightness in the space \({\mathcal D}[0,1]^ q\) are obtained.