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This article is cited in 5 papers
On the rate of convergence in the central limit theorem for semimartingales
R. Š. Lipсer, A. N. Širyaev
Moscow
Abstract:
Let $(X^n)_{n\ge 1}$ be a family of semimartingales with the canonical representation (1). Under the conditions (А), (В), (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.
Received: 08.10.1981
Citation:
R. Š. Lipсer, A. N. Širyaev, “On the rate of convergence in the central limit theorem for semimartingales”, Teor. Veroyatnost. i Primenen., 27:1 (1982), 3–14
Citation in format AMSBIB:
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\by R.~{\v S}.~Lipсer, 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
\mathnet{http://mi.mathnet.ru/tvp2241}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=645123}
\zmath{http://www.zentralblatt-math.org/zmath/search/?an=Zbl 0489.60052}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 27
\issue 1
\pages 1--13
\crossref{http://dx.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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Linking options:
http://mi.mathnet.ru/eng/tvp2241 http://mi.mathnet.ru/eng/tvp/v27/i1/p3
 Full text (in Russian):
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English version:
Theory of Probability and its Applications, 1982, 27:1, 1–13
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ISI Web of Knowledge:
A1983QB14800001
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This publication is cited in the following articles:
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В. И. Ротарь, “О суммировании независимых слагаемых в неклассической ситуации”, УМН, 37:6(228) (1982), 137–156
 ; V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 137–156 -
И. Г. Грамэ, “О скорости сходимости в центральной предельной теореме
для семимартингалов в неклассической постановке”, УМН, 41:5(251) (1986), 169–170
 ; 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  -
И. Г. Грамэ, “Нормальная аппроксимация для семимартингалов”, УМН, 42:6(258) (1987), 189–190 ; I. G. Grame, “A normal approximation for semimartingales”, Russian Math. Surveys, 42:6 (1987), 231–232
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Х. М. Маматов, И. Г. Грамэ, “О скорости сходимости в предельной теореме для стохастических интегралов по мартингалам”, УМН, 43:2(260) (1988), 143–144 ; 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
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Т. В. Облакова, “О скорости сходимости в центральной предельной теореме
для стохастических интегралов”, УМН, 44:2(266) (1989), 237–238 ; T. V. Oblakova, “On the rate of convergence in the central
limit theorem for stochastic integrals”, Russian Math. Surveys, 44:2 (1989), 289–290
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