Abstract:
Let Xn, n⩾1, be a sequence of semimartingales with triplets of local characteristics
Tn=(Bn,⟨Xcn⟩,νn) and let X be a continuous Gaussian martingale with
a triplet T=(0,⟨X⟩,0). We give conditions on the convergence of the triplets Tn to
T which are sufficient for the weak convergence of the distributions of Xn to the distribution
of X and for the weak convergence of the finite-dimensional distributions of Xn to
the corresponding finite-dimensional distributions of X.
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
\Bibitem{LipShi80}
\by R.~{\v S}.~Lip{\v{c}}er, A.~N.~{\v S}iryaev
\paper A functional central limit theorem for semimartingales
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 4
\pages 683--703
\mathnet{http://mi.mathnet.ru/tvp1225}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=595132}
\zmath{https://zbmath.org/?q=an:0471.60038|0454.60032}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 4
\pages 667--688
\crossref{https://doi.org/10.1137/1125084}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980MK50200002}
Linking options:
https://www.mathnet.ru/eng/tvp1225
https://www.mathnet.ru/eng/tvp/v25/i4/p683
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