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• W2021579142 abstract "Previous article Next article Limit Theorems for Products of Independent Random Matrices with Positive ElementsV. L. GirkoV. L. Girkohttps://doi.org/10.1137/1127092PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. L. Girko, Limit theorems for eigenvalues of products of independent random matrices with nonnegative random elements, Vychisl. Prikl. Mat. (Kiev), (1980), 29–35, 163, (In Russian.) 84b:60043 0474.60023 Google Scholar[2] V. L. Girko, On a new method for proving some limit theorems for products of independent random matrices, Theory Prob. Math. Stat., 22 (1981), 35–47 0459.60036 Google Scholar[3] V. L. Girko, A limit theorem for products of random matrices, Theory Prob. Appl., 21 (1976), 197–199 0367.60032 LinkGoogle Scholar[4] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954ix+264 16,52d 0056.36001 Google Scholar[5] A. K. Grintsevichus, On continuity of the distribution of a sum of dependent random variables associated with independent walks on lines, Theory Prob. Appl., 19 (1974), 163–168 0321.60053 LinkGoogle Scholar[6] I. Ya. Gol'dsheid, Asymptotic analysis of a product of random matrices depending on a parameter, Soviet Math. Dokl., 16 (1975), 1375–1379 Google Scholar[7] L. A. Kalenskii, Limit theorems for products of independent triangular matrices, Theory Prob. Appl., 22 (1977), 160–166 0374.60032 LinkGoogle Scholar[8] V. M. Maksimov, A generalized Bernoulli scheme and its limit distributions, Theory Prob. Appl., 18 (1973), 521–530 0299.60055 LinkGoogle Scholar[9] V. N. Tutubalin, A variant of a local limit theorem for products of random matrices, Theory Prob. Appl., 22 (1977), 203–214 0382.60019 LinkGoogle Scholar[10] V. N. Tutubalin, Representation of random matrices in orispherical coordinates and its application to telegraph equations, Theory Prob. Appl., 17 (1972), 255–268 0267.60028 LinkGoogle Scholar[11] V. N. Tutubalin, The limiting behavior of compositions of measures in certain homogeneous spaces, Izv. Akad. Nauk SSSR Ser. Mat., 27 (1963), 1301–1342, (In Russian.) 32:8393a Google Scholar[12] V. N. Tutubalin, On Limit theorems for product of random matrices, Theory Prob. Appl., 10 (1965), 15–27 LinkGoogle Scholar[13] V. N. Tutubalin, The asymptotic behavior of the distribution of a product of complex unitary matrices, Vestnik Moskov. Univ. Ser. I Mat. Meh., 21 (1966), 70–77, (In Russian.) 35:1076 Google Scholar[14] V. V. Sazonov and , V. N. Tutubalin, Probability distributions on topological groups, Theory Prob. Appl., 11 (1966), 1–45 0171.38701 LinkGoogle Scholar[15] Richard Bellman, Limit theorems for non-commutative operations. I, Duke Math. J., 21 (1954), 491–500 15,969e 0057.11202 CrossrefGoogle Scholar[16] H. Furstenberg and , H. Kesten, Products of random matrices, Ann. Math. Statist, 31 (1960), 457–469 22:12558 0137.35501 CrossrefGoogle Scholar[17] B. M. Brown and , G. K. Eagleson, Martingale convergence to infinitely divisible laws with finite variances, Trans. Amer. Math. Soc., 162 (1971), 449–453 44:6001 0228.60011 CrossrefGoogle Scholar[18] A. Kłopotowski, Limit theorems for sums of dependent random vectors in $Rsp{d}$, Dissertationes Math. (Rozprawy Mat.), 151 (1977), 58–, State Scientific Publishing House, Warsaw 57:4294 0369.60029 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Random Matrices29 September 2014 Cross Ref Spectral analysis of stochastic recurrence systems of growing dimension under G-condition. Canonical equation K 91Random Operators and Stochastic Equations, Vol. 17, No. 3 Cross Ref Random Matrices15 August 2006 Cross Ref Volume 27, Issue 4| 1983Theory of Probability & Its Applications History Submitted:14 March 1979Published online:17 July 2006 InformationCopyright © 1983 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1127092Article page range:pp. 837-844ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics" @default.
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