Weak convergence to the multiple Stratonovich integral

We have considered the problem of the weak convergence, as [var epsilon] tends to zero, of the multiple integral processesin the space , where f[set membership, variant]L2([0,T]n) is a given function, and {[eta][var epsilon](t)}[var epsilon]>0 is a family of stochastic processes with absolutely continuous paths that converges weakly to the Brownian motion. In view of the known results when n[greater-or-equal, slanted]2 and f(t1,...,tn)=1{t1<t2<...<tn}, we cannot expect that these multiple integrals converge to the multiple Itô-Wiener integral of f, because the quadratic variations of the [eta][var epsilon] are null. We have obtained the existence of the limit for any {[eta][var epsilon]}, when f is given by a multimeasure, and under some conditions on {[eta][var epsilon]} when f is a continuous function and when f(t1,...,tn)=f1(t1)...fn(tn)1{t1<t2<...<tn}, with fi[set membership, variant]L2([0,T]) for any i=1,...,n. In all these cases the limit process is the multiple Stratonovich integral of the function f.