Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 1, pp. 132-137
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R. Š. Lipcer; A. N. Širyaev. Necessary and sufficient conditions for the functional central limit theorem for semimartingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 1, pp. 132-137. http://geodesic.mathdoc.fr/item/TVP_1981_26_1_a9/
@article{TVP_1981_26_1_a9,
author = {R. \v{S}. Lipcer and A. N. \v{S}iryaev},
title = {Necessary and sufficient conditions for the functional central limit theorem for semimartingales},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {132--137},
year = {1981},
volume = {26},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_1_a9/}
}
TY - JOUR
AU - R. Š. Lipcer
AU - A. N. Širyaev
TI - Necessary and sufficient conditions for the functional central limit theorem for semimartingales
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1981
SP - 132
EP - 137
VL - 26
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1981_26_1_a9/
LA - ru
ID - TVP_1981_26_1_a9
ER -
%0 Journal Article
%A R. Š. Lipcer
%A A. N. Širyaev
%T Necessary and sufficient conditions for the functional central limit theorem for semimartingales
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1981
%P 132-137
%V 26
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1981_26_1_a9/
%G ru
%F TVP_1981_26_1_a9
Suppose that $X^n$, $n\ge 1$, is a family of semimartingales with the triplets of local characteristics $(B^n,\langle X^{nc}\rangle,\nu^n)$ and $M$ is a continuous Gaussian martingale. We find conditions which are necessary and sufficient for the weak convergence $X^n\overset{\mathscr D}{\to}M$ ($n\to\infty$).
