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Teoriya Veroyatnostei i ee Primeneniya, 1980, Volume 25, Issue 4, Pages 683–703
(Mi tvp1225)
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This article is cited in 66 scientific papers (total in 68 papers)
A functional central limit theorem for semimartingales
R. Š. Lipčer, A. N. Širyaev Moscow
Abstract:
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 $X$.
Received: 25.03.1980
Citation:
R. Š. Lipčer, A. N. Širyaev, “A functional central limit theorem for semimartingales”, Teor. Veroyatnost. i Primenen., 25:4 (1980), 683–703; Theory Probab. Appl., 25:4 (1981), 667–688
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