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Kruglov, Victor Makarovich

Statistics Math-Net.Ru
Total publications: 60
Scientific articles: 50
Presentations: 2

Number of views:
This page:1522
Abstract pages:12302
Full texts:4726
References:575
Professor
Doctor of physico-mathematical sciences (1976)
Speciality: 01.01.05 (Probability theory and mathematical statistics)
Birth date: 14.11.1937
Keywords: weak convergence (compactness) of random variables, numeric characteristics of random variables, the variance principle, the Pearson statistic.
   
Main publications:
  • Kruglov V. M. Convergence of numeric characteristics of sums of independent random variables // Lecture Notes, 1973, v. 330, 255–286.
  • Finkelstein M., Kruglov V. M., Tucker H. G. Convergence in law of random sums with non-random centering // Journal of Theoretical Probability, 1994, v. 7, № 3, 565–598.

http://www.mathnet.ru/eng/person17879
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/199757
https://www.scopus.com/authid/detail.url?authorId=7005222464

Publications in Math-Net.Ru
2020
1. D. Kh. Kazanchyan, V. M. Kruglov, “A new sufficient condition for uniform integrability of exponential local martingales”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2020, 3,  5–13  mathnet  elib
2019
2. D. Kh. Kazanchyan, V. M. Kruglov, “Uniform integrability of exponential processes”, Lobachevskii J. Math., 40:10 (2019),  1498–1506  mathnet  isi  scopus
2018
3. V. M. Kruglov, “On equivalence of predictable and natural stochastic processes”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2018, 3,  58–71  mathnet  elib
2013
4. V. M. Kruglov, “On one identity for distribution of sums of independent random variables”, Teor. Veroyatnost. i Primenen., 58:2 (2013),  396–397  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 58:2 (2014), 329–331  isi  elib  scopus
2011
5. V. M. Kruglov, “A simple proof of the unboundedness of homogeneous stochastic processes with independent increments”, Teor. Veroyatnost. i Primenen., 56:4 (2011),  806–808  mathnet  mathscinet  elib; Theory Probab. Appl., 56:4 (2011), 691–693  isi  elib  scopus
2009
6. V. M. Kruglov, “Continuity of the natural filtration of a process with independent increments”, Teor. Veroyatnost. i Primenen., 54:4 (2009),  783–789  mathnet  mathscinet; Theory Probab. Appl., 54:4 (2010), 693–699  isi  scopus
2008
7. V. M. Kruglov, “On Convergence of Submartingales”, Teor. Veroyatnost. i Primenen., 53:2 (2008),  364–373  mathnet  zmath; Theory Probab. Appl., 53:2 (2009), 321–329  isi  scopus
2007
8. V. M. Kruglov, “On the necessity of the Lyapunov condition for normal convergence”, Teor. Veroyatnost. i Primenen., 52:1 (2007),  173–175  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 52:1 (2008), 164–166  isi  scopus
2006
9. V. M. Kruglov, “Growth of sums of pairwise independent random variables with infinite means”, Teor. Veroyatnost. i Primenen., 51:2 (2006),  382–385  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 51:2 (2007), 359–362  isi  scopus
2005
10. V. M. Kruglov, “Strengthening of Prokhorov's arcsine-inequality”, Teor. Veroyatnost. i Primenen., 50:4 (2005),  767–774  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 50:4 (2006), 677–684  isi
2004
11. V. M. Kruglov, “On inequalities for large deviations in the Bernoulli scheme”, Teor. Veroyatnost. i Primenen., 49:4 (2004),  785–790  mathnet  mathscinet  zmath
2003
12. V. M. Kruglov, “Normal and Poisson convergencies”, Teor. Veroyatnost. i Primenen., 48:2 (2003),  392–398  mathnet  mathscinet  zmath; Theory Probab. Appl., 48:2 (2004), 347–355  isi
2002
13. V. M. Kruglov, “On extending the Brunk–Prokhorov strong law of large numbers”, Teor. Veroyatnost. i Primenen., 47:2 (2002),  347–349  mathnet  mathscinet  zmath; Theory Probab. Appl., 47:2 (2003), 330–333  isi
2001
14. V. M. Kruglov, “On the Necessity of the Lindeberg Condition for the Normal Convergence of Martingales”, Mat. Zametki, 70:1 (2001),  51–58  mathnet  mathscinet  zmath; Math. Notes, 70:1 (2001), 46–52  isi
15. V. M. Kruglov, G. N. Petrovskaya, “Weak Convergence of a Certain Functional”, Teor. Veroyatnost. i Primenen., 46:4 (2001),  779–784  mathnet  mathscinet  zmath; Theory Probab. Appl., 46:4 (2002), 721–727  isi
16. V. M. Kruglov, B. Zhang, “Weak Convergence of Random Sums”, Teor. Veroyatnost. i Primenen., 46:1 (2001),  28–49  mathnet  mathscinet  zmath; Theory Probab. Appl., 46:1 (2002), 39–57  isi
2000
17. V. M. Kruglov, “The asymptotic behavior of the Pearson statistic”, Teor. Veroyatnost. i Primenen., 45:1 (2000),  73–102  mathnet  mathscinet  zmath; Theory Probab. Appl., 45:1 (2001), 69–92  isi
1999
18. V. M. Kruglov, “Complete convergence of the Pearson statistic”, Mat. Zametki, 66:4 (1999),  626–629  mathnet  mathscinet; Math. Notes, 66:4 (1999), 515–519  isi
1998
19. V. M. Kruglov, “Weak compactness of random sums of independent random variables”, Teor. Veroyatnost. i Primenen., 43:2 (1998),  248–271  mathnet  mathscinet  zmath; Theory Probab. Appl., 43:2 (1999), 203–220  isi
1997
20. V. M. Kruglov, “To the invariance principle”, Teor. Veroyatnost. i Primenen., 42:2 (1997),  239–261  mathnet  mathscinet  zmath; Theory Probab. Appl., 42:2 (1998), 225–243  isi
1996
21. V. M. Kruglov, Zhang Bo, “Limit theorems for the maximal random sums”, Teor. Veroyatnost. i Primenen., 41:3 (1996),  520–532  mathnet  mathscinet  zmath; Theory Probab. Appl., 41:3 (1997), 468–478  isi
1994
22. Sh. O. Alekperov, V. M. Kruglov, “Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws”, Teor. Veroyatnost. i Primenen., 39:2 (1994),  248–271  mathnet  mathscinet  zmath; Theory Probab. Appl., 39:2 (1994), 197–216  isi
1992
23. V. M. Kruglov, “Criteria for Concentration Functions to Belong to the Domains of Attraction of Stable Laws”, Teor. Veroyatnost. i Primenen., 37:3 (1992),  459–467  mathnet  mathscinet  zmath; Theory Probab. Appl., 37:3 (1993), 424–432
1991
24. V. M. Kruglov, “Convergence of distributions of random sums to the normal and the Poisson law”, Teor. Veroyatnost. i Primenen., 36:2 (1991),  361–363  mathnet  mathscinet  zmath; Theory Probab. Appl., 36:2 (1991), 378–380  isi
1988
25. M. Sh. Braverman, V. M. Kruglov, “An Inequality for Absolute Pseudomoments”, Teor. Veroyatnost. i Primenen., 33:4 (1988),  773–777  mathnet  mathscinet  zmath; Theory Probab. Appl., 33:4 (1988), 718–722  isi
26. V. M. Kruglov, “Convergence of Moments of Random Sums”, Teor. Veroyatnost. i Primenen., 33:2 (1988),  360–363  mathnet  mathscinet  zmath; Theory Probab. Appl., 33:2 (1988), 339–342  isi
1987
27. V. M. Kruglov, A. M. Ulanovskii, “Mixtures of Probability Distributions which are Defined Uniquely by their Behaviour on Half-Axis”, Teor. Veroyatnost. i Primenen., 32:4 (1987),  670–678  mathnet  mathscinet  zmath; Theory Probab. Appl., 32:4 (1987), 608–616  isi
28. V. M. Kruglov, “Parametric Law of the Iterated Logarithm”, Teor. Veroyatnost. i Primenen., 32:1 (1987),  73–81  mathnet  mathscinet  zmath; Theory Probab. Appl., 32:1 (1987), 68–76  isi
1985
29. V. M. Kruglov, “Weak convergence of random broken lines to the Wiener process”, Teor. Veroyatnost. i Primenen., 30:2 (1985),  209–218  mathnet  mathscinet  zmath; Theory Probab. Appl., 30:2 (1986), 225–234  isi
1984
30. V. M. Kruglov, S. N. Antonov, “Once more on the asymptotic behaviour of infinitely divisible distributions in Banach space”, Teor. Veroyatnost. i Primenen., 29:4 (1984),  735–742  mathnet  mathscinet  zmath; Theory Probab. Appl., 29:4 (1985), 766–775  isi
1982
31. V. M. Kruglov, S. N. Antonov, “On the asymptotical behaviour of infinitely divisible distributions in a Banach space”, Teor. Veroyatnost. i Primenen., 27:4 (1982),  625–642  mathnet  mathscinet  zmath; Theory Probab. Appl., 27:4 (1983), 667–687  isi
1981
32. V. M. Kruglov, “Central limit theorem and the law of large numbers”, Mat. Zametki, 30:4 (1981),  583–593  mathnet  mathscinet  zmath; Math. Notes, 30:4 (1981), 786–791  isi
33. V. M. Kruglov, “Central limit theorem and the law of large numbers in the mean”, Teor. Veroyatnost. i Primenen., 26:4 (1981),  824–827  mathnet  mathscinet  zmath; Theory Probab. Appl., 26:4 (1982), 813–815  isi
1979
34. V. M. Kruglov, “A case when convergence in the mean is equivalent to convergence in the Lévy metric”, Mat. Zametki, 26:3 (1979),  483–491  mathnet  mathscinet  zmath; Math. Notes, 26:3 (1979), 732–736  isi
35. V. M. Kruglov, “The sum and the order statistics of independent random variables”, Teor. Veroyatnost. i Primenen., 24:4 (1979),  710–727  mathnet  mathscinet  zmath; Theory Probab. Appl., 24:4 (1980), 712–728  isi
1976
36. V. M. Kruglov, “A new characterization of the Poisson distribution”, Mat. Zametki, 20:6 (1976),  879–882  mathnet  mathscinet  zmath; Math. Notes, 20:6 (1976), 1049–1051
37. V. M. Kruglov, “Global limit theorems”, Teor. Veroyatnost. i Primenen., 21:1 (1976),  123–127  mathnet  mathscinet  zmath; Theory Probab. Appl., 21:1 (1976), 125–129
38. V. M. Kruglov, “Global limit theorems”, Zap. Nauchn. Sem. LOMI, 61 (1976),  84–101  mathnet  mathscinet  zmath; J. Soviet Math., 16:5 (1981), 1396–1409
1975
39. V. M. Zolotarev, V. M. Kruglov, “The structure of infinitely divisible distributions on a bicompact Abelian group”, Teor. Veroyatnost. i Primenen., 20:4 (1975),  712–724  mathnet  mathscinet  zmath; Theory Probab. Appl., 20:4 (1976), 698–709
1974
40. V. M. Kruglov, “A global limit theorem for sums of independent random variables”, Dokl. Akad. Nauk SSSR, 219:3 (1974),  542–545  mathnet  mathscinet  zmath
41. V. M. Kruglov, “Characterization of a class of infinitely divisible distributions in Hilbert space”, Mat. Zametki, 16:5 (1974),  777–782  mathnet  mathscinet  zmath; Math. Notes, 16:5 (1974), 1057–1060
42. V. M. Kruglov, “On unboundedly divisible distributions in Hilbert space”, Mat. Zametki, 16:4 (1974),  585–594  mathnet  mathscinet  zmath; Math. Notes, 16:4 (1974), 940–946
43. V. M. Kruglov, “The behaviour of sums of independent random variables”, Teor. Veroyatnost. i Primenen., 19:2 (1974),  387–391  mathnet  mathscinet  zmath; Theory Probab. Appl., 19:2 (1975), 374–379
1973
44. V. M. Kruglov, “Convergence of numerical characteristics of sums of independent random variables with vakues in a Hilbert space”, Teor. Veroyatnost. i Primenen., 18:4 (1973),  734–752  mathnet  mathscinet  zmath; Theory Probab. Appl., 18:4 (1974), 694–712
1972
45. V. M. Kryglov, “Integrals with respect to infinitely divisible distributions in a Hilbert space”, Mat. Zametki, 11:6 (1972),  669–676  mathnet  mathscinet  zmath; Math. Notes, 11:6 (1972), 407–411
46. V. M. Kruglov, “On an extension of the class of stable distributions”, Teor. Veroyatnost. i Primenen., 17:4 (1972),  723–732  mathnet  mathscinet  zmath; Theory Probab. Appl., 17:4 (1973), 685–694
47. V. M. Kruglov, “Limit theorems for sums of independent random variables with values in Hilbert space”, Teor. Veroyatnost. i Primenen., 17:2 (1972),  209–227  mathnet  mathscinet  zmath; Theory Probab. Appl., 17:2 (1973), 199–217
1971
48. V. M. Kruglov, “Convergence of distributions of sums of independent random variables with values in a Hilbert space to the normal and Poisson distributions”, Dokl. Akad. Nauk SSSR, 197:6 (1971),  1258–1260  mathnet  mathscinet  zmath
49. V. M. Kruglov, “Convergence of distributions of sums of independent Hilbert-space-valued random variables”, Teor. Veroyatnost. i Primenen., 16:2 (1971),  346–347  mathnet  mathscinet  zmath; Theory Probab. Appl., 16:2 (1971), 350–351
1970
50. V. M. Kruglov, “A note to the theory of infinite divisible laws”, Teor. Veroyatnost. i Primenen., 15:2 (1970),  330–336  mathnet  mathscinet  zmath; Theory Probab. Appl., 15:2 (1970), 319–324
1968
51. V. M. Kruglov, “A local limit theorem for unequally distributed random variables”, Teor. Veroyatnost. i Primenen., 13:2 (1968),  348–351  mathnet  mathscinet  zmath; Theory Probab. Appl., 13:2 (1968), 332–334

2006
52. V. M. Kruglov, “Yakimiv A. L. Probabilistic Applications of Tauberian Theorems”, Teor. Veroyatnost. i Primenen., 51:4 (2006),  822–824  mathnet  elib; Theory Probab. Appl., 51:4 (2007), 737–738
53. L. G. Afanas'eva, E. V. Bulinskaya, O. V. Viskov, I. È. Ibragimov, R. I. Ivanovskaya, V. Yu. Korolev, V. M. Kruglov, Yu. V. Prokhorov, B. A. Sevast'yanov, V. V. Senatov, M. V. Khatuntseva, Yu. S. Khokhlov, D. M. Chibisov, A. N. Shiryaev, “On the 75th birthday of V. M. Zolotarev”, Teor. Veroyatnost. i Primenen., 51:4 (2006),  773–775  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 51:4 (2007), 680–682  isi
2001
54. V. M. Kruglov, “Book review: Bañuelos R., Moore C. N. “Probabilistic behavior of Harmonic Functions””, Teor. Veroyatnost. i Primenen., 46:2 (2001),  411–413  mathnet; Theory Probab. Appl., 46:2 (2002), 383–385
1999
55. V. M. Kruglov, “Book review: Vladimir M. Zolotarev “Modern Theory of Summation of Random Variables””, Teor. Veroyatnost. i Primenen., 44:2 (1999),  473–475  mathnet; Theory Probab. Appl., 4:2 (2000), 428–431
1997
56. V. M. Kruglov, “Book review: Fristedt В., Gray L. “A modern approach to probability theory””, Teor. Veroyatnost. i Primenen., 42:3 (1997),  650–652  mathnet
1986
57. V. M. Kruglov, S. N. Antonov, “Letter to the editors”, Teor. Veroyatnost. i Primenen., 31:1 (1986),  188  mathnet  mathscinet; Theory Probab. Appl., 31:1 (1987), 175
1981
58. V. M. Kruglov, “Ian F. Blake «Аn introduction to applied probability» (book review)”, Teor. Veroyatnost. i Primenen., 26:2 (1981),  434–435  mathnet; Theory Probab. Appl., 26:2 (1982), 424–431
59. V. M. Kruglov, “P. Billingsley «Probability and Measure» (book review)”, Teor. Veroyatnost. i Primenen., 26:1 (1981),  219–220  mathnet; Theory Probab. Appl., 26:1 (1981), 212–215
1980
60. V. M. Kruglov, “A. Mukherjea and К. Pothoven, «Real and functional analysis» (book review)”, Teor. Veroyatnost. i Primenen., 25:1 (1980),  219–220  mathnet; Theory Probab. Appl., 25:1 (1980), 216–217
1971
61. V. M. Kruglov, “Addendum: A Note on Infinitely Divisible Distributions”, Teor. Veroyatnost. i Primenen., 16:2 (1971),  401  mathnet  mathscinet; Theory Probab. Appl., 16:2 (1971), 397

Presentations in Math-Net.Ru
1. Об эквивалентности достаточных условий сходимости мартингалов
V. M. Kruglov
Principle Seminar of the Department of Probability Theory, Moscow State University
December 6, 2006
2. Усиленный закон больших чисел
V. M. Kruglov
Principle Seminar of the Department of Probability Theory, Moscow State University
March 9, 2005

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