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Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 3, Pages 535–561 (Mi tvp3900)  

This article is cited in 11 scientific papers (total in 11 papers)

Multidimensional Version of a Result of Sakhanenko in the Invariance Principle for Vectors with Finite Exponential Moments. II

A. Yu. Zaitsev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: A multidimensional version of a result of Sakhanenko for the Gaussian approximation of sequences of successive sums of independent nonidentically distributed random vectors with finite exponential moments is obtained.

Keywords: multidimensional invariance principle, strong approximation, sums of independent nonidentically distributed random vectors.

DOI: https://doi.org/10.4213/tvp3900

Full text: PDF file (2145 kB)

English version:
Theory of Probability and its Applications, 2002, 46:3, 490–514

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Received: 07.09.1998
Language:

Citation: A. Yu. Zaitsev, “Multidimensional Version of a Result of Sakhanenko in the Invariance Principle for Vectors with Finite Exponential Moments. II”, Teor. Veroyatnost. i Primenen., 46:3 (2001), 535–561; Theory Probab. Appl., 46:3 (2002), 490–514

Citation in format AMSBIB
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\pages 490--514
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    This publication is cited in the following articles:
    1. Zaitsev A.Yu., “Estimates of the rate of approximation in a de-Poissonization lemma”, Ann. Inst. H. Poincaré Probab. Statist., 38:6 (2002), 1071–1086  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Zaitsev A.Yu., “Estimates of the rate of approximation in the CLT for $L_1$-norm of density estimators”, High dimensional probability, III (Sandjberg, 2002), Progr. Probab., 55, Birkhäuser, Basel, 2003, 255–292  mathscinet  zmath  isi
    3. A. Yu. Zaitsev, “Estimates for the rate of strong approximation in the multidimensional invariance principle”, J. Math. Sci. (N. Y.), 145:2 (2007), 4856–4865  mathnet  crossref  mathscinet  zmath
    4. A. Yu. Zaitsev, “Estimates for the rate of strong Gaussian approximation for the sums of i.i.d. multidimensional random vectors”, J. Math. Sci. (N. Y.), 152:6 (2008), 875–884  mathnet  crossref
    5. Theory Probab. Appl., 53:1 (2009), 59–80  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. A. Yu. Zaitsev, “The rate of Gaussian strong approximation for the sums of i.i.d. multidimensional random vectors”, J. Math. Sci. (N. Y.), 163:4 (2010), 399–408  mathnet  crossref
    7. Wu Wei Biao, Zhou Zhou, “Gaussian approximations for non-stationary multiple time series”, Statist. Sinica, 21:3 (2011), 1397–1413  crossref  mathscinet  zmath  isi  scopus
    8. Chatterjee S., “A new approach to strong embeddings”, Probab. Theory Relat. Fields, 152:1-2 (2012), 231–264  crossref  mathscinet  zmath  isi  scopus
    9. A. Yu. Zaitsev, “The accuracy of strong Gaussian approximation for sums of independent random vectors”, Russian Math. Surveys, 68:4 (2013), 721–761  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Wu W. Zhou Zh., “Simultaneous Quantile Inference For Non-Stationary Long-Memory Time Series”, Bernoulli, 24:4A (2018), 2991–3012  crossref  mathscinet  zmath  isi  scopus
    11. Lifshits M.A. Nikitin Ya.Yu. Petrov V.V. Zaitsev A.Yu. Zinger A.A., “Toward the History of the Saint Petersburg School of Probability and Statistics. i. Limit Theorems For Sums of Independent Random Variables”, Vestnik St. Petersburg Univ. Math., 51:2 (2018), 144–163  crossref  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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