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Uspekhi Mat. Nauk, 1995, Volume 50, Issue 5(305), Pages 3–62 (Mi umn1104)  

This article is cited in 20 scientific papers (total in 20 papers)

The Khintchine inequalities and martingale expanding sphere of their action

G. Peškir, A. N. Shiryaeva

a Steklov Mathematical Institute, Russian Academy of Sciences

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English version:
Russian Mathematical Surveys, 1995, 50:5, 849–904

Bibliographic databases:

UDC: 519.21
MSC: 60G50, 46E30, 60E15
Received: 05.01.1995

Citation: G. Peškir, A. N. Shiryaev, “The Khintchine inequalities and martingale expanding sphere of their action”, Uspekhi Mat. Nauk, 50:5(305) (1995), 3–62; Russian Math. Surveys, 50:5 (1995), 849–904

Citation in format AMSBIB
\by G.~Pe{\v s}kir, A.~N.~Shiryaev
\paper The Khintchine inequalities and martingale expanding sphere of their action
\jour Uspekhi Mat. Nauk
\yr 1995
\vol 50
\issue 5(305)
\pages 3--62
\jour Russian Math. Surveys
\yr 1995
\vol 50
\issue 5
\pages 849--904

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    This publication is cited in the following articles:
    1. P. V. Il'in, “A generalization of Khinchin's inequalities to the case of quadratic forms”, Russian Math. Surveys, 54:6 (1999), 1244–1245  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Sh. Sharakhmetov, R. Ibragimov, “The Exact Constant in the Rosenthal Inequality for Random Variables with Mean Zero”, Theory Probab Appl, 46:1 (2002), 127  mathnet  crossref  mathscinet  isi  elib
    3. S. Louhichi, “Moment Inequalities for Sums of Certain Dependent Random Variables”, Theory Probab Appl, 47:4 (2003), 649  mathnet  crossref  mathscinet  zmath  isi  elib
    4. Yu. L. Botnikov, “Davis-type inequalities for a number of diffusion processes”, J. Math. Sci. (N. Y.), 137:1 (2006), 4502–4509  mathnet  crossref  mathscinet  zmath  elib
    5. S. V. Nagaev, “On probability and moment inequalities for supermartingales and martingales”, Theory Probab. Appl., 51:2 (2007), 367–377  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. E. L. Presman, “Estimation of the Constant in a Burkholder Inequality for Supermartingales and Martingales”, Theory Probab. Appl., 53:1 (2009), 173–179  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. S. V. Astashkin, “A Generalized Khintchine Inequality in Rearrangement Invariant Spaces”, Funct. Anal. Appl., 42:2 (2008), 144–147  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. S. V. Astashkin, “Independent functions in rearrangement invariant spaces and the Kruglov property”, Sb. Math., 199:7 (2008), 945–963  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. GÖtz E. Pfander, Holger Rauhut, Jared Tanner, “Identification of Matrices Having a Sparse Representation”, IEEE Trans Signal Process, 56:11 (2008), 5376  crossref  mathscinet  isi
    10. Joel A. Tropp, “On the conditioning of random subdictionaries”, Applied and Computational Harmonic Analysis, 25:1 (2008), 1  crossref
    11. Anthony Man-Cho So, “Moment inequalities for sums of random matrices and their applications in optimization”, Math Program, 2009  crossref
    12. S. V. Astashkin, “Rademacher functions in symmetric spaces”, Journal of Mathematical Sciences, 169:6 (2010), 725–886  mathnet  crossref  mathscinet  zmath  elib
    13. Yong Jiao, Tao Ma, Peide Liu, “Embeddings of Lorentz Spaces of Vector-Valued Martingales”, Funct. Anal. Appl., 44:3 (2010), 237–240  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. S. V. Astashkin, “Vector-valued sums of independent functions in rearrangement invariant spaces”, Siberian Math. J., 51:4 (2010), 584–594  mathnet  crossref  mathscinet  isi  elib  elib
    15. S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. M. M. Skriganov, “Khinchin's inequality and Chen's theorem”, St. Petersburg Math. J., 23:4 (2012), 761–778  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    17. S. V. Astashkin, “Rosenthal type inequalities for martingales in symmetric spaces”, Russian Math. (Iz. VUZ), 56:11 (2012), 52–57  mathnet  crossref  mathscinet
    18. Pinelis I., “An Asymptotically Gaussian Bound on the Rademacher Tails”, Electron. J. Probab., 17 (2012), 35, 1–22  crossref  isi
    19. S. V. Astashkin, “Martingale Rosenthal inequalities in symmetric spaces”, Sb. Math., 205:12 (2014), 1720–1740  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. Jiao Y. Sukochev F. Zanin D., “Sums of Independent and Freely Independent Identically Distributed Random Variables”, Studia Math., 251:3 (2020), 289–315  crossref  isi
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