On the invariance principle for semimartingales with «nonclassical» assumptions

Suppose that $X^n$, $n\ge 1$, is a family of semimartingales with triplets of local characteristics $(B^n,\langle X^{nc}\rangle,\nu^n)$ and let $M$ be a Gaussian martingale. We find conditions (theorem 2) which are sufficient for the weak convergence $X^n$ to $M$.