On properties of polynomials in random elements

V. V. Ulyanov

Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 2, pp. 391-402

Bibliographie

[1] Götze F., “Asymptotic expansions for bivariate von Mises functionals”, Z. Wahrscheinlichkeitstheor. verw. Geb., 50:3 (1979), 333-–355 | DOI | MR | Zbl

[2] Götze F., “Edgeworth expansions in functional limit theorems”, Ann. Probab., 17:4 (1989), 1602–1634 | DOI | MR | Zbl

[3] Weyl H., “Über die Gleichverteilung von Zahlen mod. Eins”, Math. Ann., 77:3 (1916), 313–352 | DOI | MR | Zbl

[4] Yurinskii V. V., “Otsenka pogreshnosti normalnogo priblizheniya veroyatnosti popadaniya v shar”, Dokl. AN SSSR, 258 (1981), 577–578

[5] Yurinskii V. V., “O pogreshnosti normalnogo priblizheniya”, Sib. matem. zhurn., 24:6 (1983), 188–199 | MR | Zbl

[6] Gëttse F., Prokhorov Yu. V., Ulyanov V. V., “Otsenki dlya kharakteristicheskikh funktsii mnogochlenov ot asimptoticheski normalnykh sluchainykh velichin”, Uspekhi matem. nauk, 51:2 (1996), 3–26 | DOI | MR

[7] Gëttse F., Prokhorov Yu. V., Ulyanov V. V., “O gladkom povedenii veroyatnostnykh raspredelenii pri polinomialnykh otobrazheniyakh”, Teoriya veroyatn. i ee primen., 42:1 (1997), 51–62 | DOI | MR | Zbl

[8] Götze F., Prohorov V. V., Ulyanov V. V., “A stochastic analogue of the Vinogradov mean value theorem”, Probability Theory and Mathematical Statistics (Tokyo, 1995), World Scientific, River Edge, 1996, 62–82 | MR | Zbl

[9] Prokhorov Yu. V., Kristof G., Ulyanov V. V., “O kharakterizatsionnykh svoistvakh kvadratichnykh form”, Dokl. RAN, 373:2 (2000), 168–170 | MR | Zbl

[10] Christoph G., Prohorov Yu., Ulyanov V., “Characterization and stability problems for finite quadratic forms”, Asymptotic Methods in Probability and Statistics with Applications (St. Petersburg, 1998), Birkhäuser, Boston, 2001, 39–50 | DOI | MR | Zbl

[11] Prokhorov Yu. V., Kristof G., Ulyanov V. V., “O raspredelenii kvadratichnykh form ot gaussovskikh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 40:2 (1995), 301–312 | MR | Zbl

[12] Prokhorov Yu. V., Ulyanov V. V., “Some approximation problems in statistics and probability”, Limit Theorems in Probability, Statistics and Number Theory, Springer Proc. Math. Statist., 42, Springer, Heidelberg, 2013, 235–249 | MR | Zbl

[13] Prokhorov Yu. V., Izbrannye trudy, Torus-Press, M., 2012, 778 pp.

[14] Rudin W., Fourier Analysis on Groups, Interscience Publ., New York, 1962, 285 pp. | MR | Zbl

[15] Gelfand I. M., Raikov D. A., Shilov G. E., “Kommutativnye normirovannye koltsa”, Uspekhi matem. nauk, 1:2 (1946), 48–146 | MR | Zbl

[16] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965, 615 pp.; т. 2, 537 с.

[17] Wiener N., Wintner A., “Fourier–Stieltjes transforms and singular infinite convolutions”, Amer. J. Math., 60:3 (1938), 513–522 | DOI | MR

[18] Salem R., “On singular monotonic functions of the Cantor type”, J. Math. Phys. Mass. Inst. Tech., 21 (1942), 69–82 | MR | Zbl

[19] Schaeffer A. C., “The Fourier–Stieltjes coefficients of a function of bounded variation”, Amer. J. Math., 61 (1939), 934–940 | DOI | MR

[20] Prachar K., Primzahlverteilung, Springer-Verlag, Berlin, 1978, 421 pp. | MR | Zbl

[21] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980, 144 pp.

[22] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987, 368 pp.

[23] Stechkin S. B., “O srednikh znacheniyakh modulya trigonometricheskoi summy”, Tr. MIAN SSSR, 134, 1975, 283–309 | MR | Zbl

[24] Wooley T. D., “Vinogradov's mean value theorem via efficient congruencing”, Ann. Math., 175:3 (2012), 1575–1627 | DOI | MR | Zbl

[25] Parsell S. T., Prendiville S. M., Wooley T. D., “Near-optimal mean value estimates for multidimensional Weyl sums”, Geom. Funct. Anal., 23:6 (2013), 1962–2024 | DOI | MR | Zbl

[26] Linnik U. V., “On Weyl's sums”, Matem. sb., 12:1 (1943), 28–39 | MR | Zbl

[27] Linnik Yu. V., Ostrovskii I. V., Razlozheniya sluchainykh velichin i vektorov, Nauka, M., 1972, 479 pp.

[28] Lukacs E., Laha R. G., Applications of characteristic functions, Griffin, London, 1964, 202 pp. | MR | Zbl

[29] Lukach E., Kharakteristicheskie funktsii, Nauka, M., 1979, 423 pp.

[30] Shohat J. A., Tamarkin J. D., The Problem of Moments, Amer. Math. Soc., Providence, 1963, 144 pp. | MR | Zbl

[31] Akhiezer N. I., Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, Fizmatgiz, M., 1961, 310 pp.

[32] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984, 752 pp.

[33] Stoyanov I., Kontrprimery v teorii veroyatnostei, Faktorial, M., 1999, 288 pp.

[34] I. M. Vinogradov (red.), Matematicheskaya entsiklopediya, v. 3, Sovetskaya entsiklopediya, M., 1982, 1184 pp.

[35] Ulyanov V. V., “Nonuniform estimates of the density of the squared norm of a Gaussian vector in Hilbert space”, New Trends in Probability and Statistics, v. 1, eds. V. Sazonov, T. Shervashidze, VSP/Mokslas, Utrecht/Vilnius, 1991, 255–263 | MR

[36] Ulyanov V. V., “On Gaussian measure of balls in $H$”, Frontiers in Pure and Applied Probability, Proceedings of the Fourth Russian-Finnish Symposium on Probability Theory and Mathematical Statistics, v. II, ed. A. N. Shiryaev et al., TVP Science Publishers, M., 1996, 195–206 | Zbl

[37] Rozovskii L. V., “O gaussovoi mere sharov v gilbertovom prostranstve”, Teoriya veroyatn. i ee primen., 53:2 (2008), 382–390 | DOI