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Mat. Sb. (N.S.), 1957, Volume 42(84), Number 1, Pages 11–44 (Mi msb5043)  

This article is cited in 18 scientific papers (total in 18 papers)

On the probability of large deviations of random magnitudes

I. N. Sanov


Full text: PDF file (2466 kB)

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Received: 24.02.1956

Citation: I. N. Sanov, “On the probability of large deviations of random magnitudes”, Mat. Sb. (N.S.), 42(84):1 (1957), 11–44

Citation in format AMSBIB
\Bibitem{San57}
\by I.~N.~Sanov
\paper On the probability of large deviations of random magnitudes
\jour Mat. Sb. (N.S.)
\yr 1957
\vol 42(84)
\issue 1
\pages 11--44
\mathnet{http://mi.mathnet.ru/msb5043}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=88087}
\zmath{https://zbmath.org/?q=an:0078.31202}


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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. N. N. Chentsov, “Invariantnye funktsii poter v zadachakh matematicheskoi statistiki”, UMN, 22:1(133) (1967), 178–180  mathnet  mathscinet
    2. V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. S. V. Nagaev, V. I. Chebotarev, “On the Accuracy of Gaussian Approximation in Hilbert Space”, Siberian Adv. Math., 15:1 (2005), 11–73  mathnet  mathscinet  zmath  elib
    4. A. A. Borovkov, “Large Sample Change-Point Estimation when Distributions Are Unknown”, Theory Probab. Appl., 53:3 (2009), 402–418  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. A. A. Borovkov, A. A. Mogul'skiǐ, “On large deviation principles in metric spaces”, Siberian Math. J., 51:6 (2010), 989–1003  mathnet  crossref  mathscinet  isi  elib
    6. S. Z. Adzhiev, V. V. Vedenyapin, “Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model”, Comput. Math. Math. Phys., 51:11 (2011), 1942–1952  mathnet  crossref  mathscinet  isi
    7. Theory Probab. Appl., 57:2 (2013), 347–357  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A. A. Borovkov, A. A. Mogulskii, “Large deviation principles for random walk trajectories. III”, Theory Probab. Appl., 58:1 (2014), 25–37  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. M. S. Ermakov, “Large Deviation Principle for moderate deviation probabilities of empirical bootstrap measure”, J. Math. Sci. (N. Y.), 204:1 (2015), 90–115  mathnet  crossref  mathscinet
    10. V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Russian Math. Surveys, 69:6 (2014), 995–1029  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. V. I. Bakhtin, “Spectral potential, Kullback action, and large deviations of empirical measures on measurable spaces”, Theory Probab. Appl., 59:4 (2015), 535–544  mathnet  crossref  crossref  mathscinet  isi  elib
    12. A. V. Gasnikov, D. Yu. Dmitriev, “On efficient randomized algorithms for finding the PageRank vector”, Comput. Math. Math. Phys., 55:3 (2015), 349–365  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. V. V. Breer, A. D. Rogatkin, “Probabilistic model of threshold behavior in multiagent systems”, Autom. Remote Control, 76:8 (2015), 1369–1386  mathnet  crossref  isi  elib  elib
    14. V. I. Bakhtin, “Spektralnyi potentsial, deistvie Kulbaka i printsip bolshikh uklonenii dlya konechno-additivnykh mer”, Tr. In-ta matem., 23:2 (2015), 11–23  mathnet
    15. A. V. Gasnikov, E. V. Gasnikova, M. A. Mendel, K. V. Chepurchenko, “Evolyutsionnye vyvody entropiinoi modeli rascheta matritsy korrespondentsii”, Matem. modelirovanie, 28:4 (2016), 111–124  mathnet  elib
    16. A. Gasnikov, E. Gasnikova, P. Dvurechensky, A. Mohammed, E. Chernousova, “About the power law of the PageRank vector distribution. Part 1. Numerical methods for finding the PageRank vector”, Num. Anal. Appl., 10:4 (2017), 299–312  mathnet  crossref  crossref  isi  elib
    17. A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Num. Anal. Appl., 11:1 (2018), 16–32  mathnet  crossref  crossref  isi  elib
    18. V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Entropiya po Boltsmanu i Puankare, ekstremali Boltsmana i metod Gamiltona–Yakobi v negamiltonovoi situatsii”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 37–59  mathnet  crossref
  • Математический сборник (новая серия) - 1947–1963
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