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Teor. Veroyatnost. i Primenen., 1982, Volume 27, Issue 1, Pages 3–14 (Mi tvp2241)  

This article is cited in 6 scientific papers (total in 6 papers)

On the rate of convergence in the central limit theorem for semimartingales

R. Š. Liper, A. N. Širyaev

Moscow

Abstract: Let $(X^n)_{n\ge 1}$ be a family of semimartingales with the canonical representation (1). Under the conditions (), (), (C) the central limit theorem is valid:
$$ R_t^n=\sup_x|\mathbf P\{X_t^n\le x\}-\Phi(\frac{x}{\sqrt V_t})|\to0,\qquad n\to\infty. $$
We give the estimates (3)–(6) for the rate of convergence of $R_t^n$ in the cases when $(X^n)_{n\ge 1}$ are families of semimartingales, local martingales and local square integrable martingales.

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English version:
Theory of Probability and its Applications, 1982, 27:1, 1–13

Bibliographic databases:

Received: 08.10.1981

Citation: R. Š. Liper, A. N. Širyaev, “On the rate of convergence in the central limit theorem for semimartingales”, Teor. Veroyatnost. i Primenen., 27:1 (1982), 3–14; Theory Probab. Appl., 27:1 (1982), 1–13

Citation in format AMSBIB
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\by R.~{\v S}.~Liper, A.~N.~{\v S}iryaev
\paper On the rate of convergence in the central limit theorem for semimartingales
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 1
\pages 3--14
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=645123}
\zmath{https://zbmath.org/?q=an:0499.60040|0489.60052}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 27
\issue 1
\pages 1--13
\crossref{https://doi.org/10.1137/1127001}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983QB14800001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 137–156  mathnet  crossref  mathscinet  zmath  zmath  isi
    2. I. G. Grame, “The rate of convergence in the central limit theorem for semimartingales in its non-classical formulation”, Russian Math. Surveys, 41:5 (1986), 143–144  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. I. G. Grame, “A normal approximation for semimartingales”, Russian Math. Surveys, 42:6 (1987), 231–232  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Kh. M. Mamatov, I. G. Grame, “On the rate of convergence in the limit theorem for stochastic integrals with respect to martingales”, Russian Math. Surveys, 43:2 (1988), 175–176  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. T. V. Oblakova, “On the rate of convergence in the central limit theorem for stochastic integrals”, Russian Math. Surveys, 44:2 (1989), 289–290  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. E. Valkeila, “On normal approximation of a process with independent increments”, Russian Math. Surveys, 50:5 (1995), 945–961  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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