Weak convergence of stochastic integrals

Let W-n = {W-n(t): t=0} n=0, be a sequence of adapted cadlag stochastic processes such that for each n=0, W-n is a semimartingale, and (W-n,[W-n])-->(W-0,V-0) weakly, in the Skorokhod space D(R+;R-2) as n --> infinity where V-0 is some a.s. nondecreasing process. We show that Z(n)(.) = integral(0)(.)f(W-n(t-)) dW(n)(t) converges weakly in D(R+,R) to the process incf(W-0(t-)) dW(0)(t) + 2(-1) integral(0)(.)f'(W-0(t-)) d[W-0](t) - 2(-1) integral(0)(.)f'(W-0(t-)) dV(0)(t) for any analytic function f on R. Here [W-n] denotes the quadratic variation of the semimartingale W-n.