A functional central limit theorem for semimartingales

R. Š. Lipčer   ; A. N. Širyaev

Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 683-703

Résumé

Let $X^n$, $n\geqslant 1$, be a sequence of semimartingales with triplets of local characteristics $T^n=(B^n,\langle X^{cn}\rangle,\nu^n)$ and let $X$ be a continuous Gaussian martingale with a triplet $T=(0,\langle X\rangle,0)$. We give conditions on the convergence of the triplets $T^n$ to $T$ which are sufficient for the weak convergence of the distributions of $X^n$ to the distribution of $X$ and for the weak convergence of the finite-dimensional distributions of $X^n$ to the corresponding finite-dimensional distributions of $X$.