|
|
|
|
Литература
|
|
| |
| 1. |
V. Bentkus, “Asymptotic expansions for distributions of sums of independent random elements in a Hilbert space”, Lithuanian Math. J., 24 (1984), 305–319    |
| 2. |
В. Бенткус, Ф. Гетце, “О числе целых точек в большом эллипсоиде”, Доклады РАН, 343:4 (1995), 439–440  |
| 3. |
V. Bentkus, F. Götze, Optimal rates of convergence in functional limit theorems for quadratic forms, Preprint 95-091 SFB 343, Universität Bielefeld, 1995 |
| 4. |
V. Bentkus, F. Götze, “Optimal rates of convergence in the CLT for quadratic forms”, Ann. Probab., 24:1 (1996), 466–490  |
| 5. |
V. Bentkus, F. Götze, “Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces”, Probab. Theory Rel. Fields, 109:3 (1997), 367–416 |
| 6. |
V. Bentkus, F. Götze, “On the lattice point problem for ellipsoids”, Acta Arithmetica, 80:2 (1997), 101–125 |
| 7. |
В. Бенткус, Ф. Гëтце, В. Паулаускас, А. Рачкаускас, “Точность гауссовской аппроксимации в банаховых пространствах”, Итоги науки и техн. Сер. Современные проблемы математики. Фундаментальные направления, 81, 1991, 39–139 |
| 8. |
V. Bentkus, F. Götze, A. Yu. Zaitsev, “Approximations of quadratic forms of independent random vectors by accompanying laws”, Теория вероятн. и ее примен., 42:2 (1997), 308–335 |
| 9. |
V. Bentkus, F. Götze, R. Zitikis, “Asymptotic expansions in the integral and local limit theorems in Banach spaces with applications to $\omega$-statistics”, J. Theor. Probab., 6:4 (1993), 727–780 |
| 10. |
R. N. Bhattacharya, R. Ranga Rao, Normal Approximation and Asymptotic Expansions, Wiley, New York, 1986 |
| 11. |
S. A. Bogatyrev, F. Götze, V. V. Ulyanov, “Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space”, J. Multivariate Anal., 97:9 (2006), 2041–2056  |
| 12. |
J. W. S. Cassels, An introduction to the geometry of numbers, Springer, Berlin–Göttingen–Heidelberg, 1959 |
| 13. |
H. Davenport, “Indefinite quadratic forms in many variables. II”, Proc. London Math. Soc., 8:3 (1958), 109–126 |
| 14. |
C.-G. Esseen, “Fourier analysis of distribution functions”, Acta Math., 77 (1945), 1–125 |
| 15. |
F. Fricker, Einführung in die Gitterpunktlehre, Birkhäuser, Basel–Boston–Stuttgart, 1982 |
| 16. |
F. Götze, “Asymptotic expansions for bivariate von Mises functionals”, Z. Wahrsch. verw. Geb., 50 (1979), 333–355 |
| 17. |
F. Götze, “Lattice point problem and values of quadratic forms”, Invent. Math., 157:1 (2004), 195–226  |
| 18. |
F. Götze, G. A. Margulis, Distribution of values of quadratic forms at integral points, Preprint, 2010, arXiv: 1004.5123 |
| 19. |
F. Götze, V. Ulyanov, Uniform approximations in the CLT for balls in Euclidian spaces, Preprint 00-034 SFB 343, Universität Bielefeld, Bielefeld, 2000 |
| 20. |
F. Götze, V. Ulyanov, Asymptotic disrtribution of $\chi^2$-type statistics, Preprint 03-033, Research group “Spectral analysis, asymptotic distributions and stochastic dynamics”, 2003 |
| 21. |
F. Götze, A. Yu. Zaitsev, Uniform rates of convergence in the CLT for quadratic forms, Preprint 08119 SFB 701, Universität Bielefeld, Bielefeld, 2008 |
| 22. |
F. Götze, A. Yu. Zaitsev, Uniform rates of approximation by short asymptotic expansions in the CLT for quadratic forms of sums of i.i.d. random vectors, Preprint 09073 SFB 701, Universität Bielefeld, Bielefeld, 2009 |
| 23. |
F. Götze, A. Yu. Zaitsev, Uniform rates of approximation by short asymptotic expansions in the CLT for quadratic forms of sums of i.i.d. random vectors, Preprint 10086 SFB 701, Universität Bielefeld, Bielefeld, 2010 |
| 24. |
G. H. Hardy, “The average order of the arithmetical functions $P(x)$ and $\Delta (x)$”, Proc. London Math. Soc., 15:2 (1916), 192–213 |
| 25. |
A. K. Lenstra, H. W. Lenstra (Jr.), L. Lovász, “Factoring polynomials with rational coefficients”, Math. Ann., 261:4 (1982), 515–534 |
| 26. |
D. Mumford, Tata Lectures on Theta, v. I, Birkhäuser, Boston–Basel–Stuttgart, 1983 |
| 27. |
S. V. Nagaev, “On a new approach to the study of the distribution of the norm of random element in Hilbert space”, Abstracts of the Fifth Intern. Vilnius Conf. in Probab. Theory and Math. Statistics, v. 4, Mokslas, VSP, Vilnius, 1989, 77–78 |
| 28. |
S. V. Nagaev, V. I. Chebotarev, “On the accuracy of Gaussian approximation in Hilbert space”, Limit theorems of probability theory (Vilnius, 1999), Acta Appl. Math., 58, 1999, 1–3, 189–215 |
| 29. |
S. V. Nagaev, V. I. Chebotarev, “On the accuracy of Gaussian approximation in Hilbert space”, Siberian Adv. Math., 15:1 (2005), 11–73 |
| 30. |
В. В. Петров, Суммы независимых случайных величин, Наука, М., 1972 |
| 31. |
H. Prawitz, “Limits for a distribution, if the characteristic function is given in a finite domain”, Skand. AktuarTidskr., 1972, 138–154 |
| 32. |
В. В. Сенатов, “Качественные эффекты в оценках скорости сходимости в центральной предельной теореме в многомерных пространствах”, Труды МИАН, 215, 1997, 3–239 |
| 33. |
V. V. Senatov, Normal approximation: new results, methods and problems, Modern Probability and Statistics, VSP, Utrecht, 1998 |
| 34. |
H. Weyl, “Über die Gleichverteilung der Zahlen mod-Eins”, Math. Ann., 77 (1915/16), 313–352 |
| 35. |
Б. А. Залесский, В. В. Сазонов, В. В. Ульянов, “Нормальная аппроксимация в гильбертовом пространстве. I”, Теория вероятн. и ее примен., 33:2 (1988), 225–245 ; “II”, 33:3 (1988), 508–521 |
