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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 1, Pages 132–137 (Mi tvp2475)  

This article is cited in 4 scientific papers (total in 5 papers)

Short Communications

Necessary and sufficient conditions for the functional central limit theorem for semimartingales

R. Š. Lipcer, A. N. Širyaev

Moscow

Abstract: 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 $X^n\overset{\mathscr D}{\to}M$ ($n\to\infty$).

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English version:
Theory of Probability and its Applications, 1981, 26:1, 130–135

Bibliographic databases:

Received: 17.09.1980

Citation: R. Š. Lipcer, A. N. Širyaev, “Necessary and sufficient conditions for the functional central limit theorem for semimartingales”, Teor. Veroyatnost. i Primenen., 26:1 (1981), 132–137; Theory Probab. Appl., 26:1 (1981), 130–135

Citation in format AMSBIB
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\by R.~{\v S}.~Lipcer, A.~N.~{\v S}iryaev
\paper Necessary and sufficient conditions for the functional central limit theorem for semimartingales
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 1
\pages 132--137
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\zmath{https://zbmath.org/?q=an:0473.60031|0458.60017}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 26
\issue 1
\pages 130--135
\crossref{https://doi.org/10.1137/1126010}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. Sh. Liptser, A. N. Shiryaev, “On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments”, Math. USSR-Sb., 44:3 (1983), 299–323  mathnet  crossref  mathscinet  zmath
    2. R. Sh. Liptser, A. N. Shiryaev, “Weak convergence of a sequence of semimartingales to a process of diffusion type”, Math. USSR-Sb., 49:1 (1984), 171–195  mathnet  crossref  mathscinet  zmath
    3. P. A. Yaskov, “Necessary conditions in the law of large numbers for martingales and associated systems”, Russian Math. Surveys, 66:4 (2011), 822–824  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. P. A. Yaskov, “On the law of large numbers for martingales”, Proc. Steklov Inst. Math., 287:1 (2014), 289–298  mathnet  crossref  crossref  isi  elib  elib
    5. V. M. Abramov, B. M. Miller, E. Ya. Rubinovich, P. Yu. Chiganskii, “Razvitie teorii stokhasticheskogo upravleniya i filtratsii v rabotakh R. Sh. Liptsera”, Avtomat. i telemekh., 2020, no. 3, 3–13  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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