@article{TVP_2009_54_3_a4,
author = {G. M. Feldman},
title = {Independent linear statistics on a-adic solenoids},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {515--532},
year = {2009},
volume = {54},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a4/}
}
G. M. Feldman. Independent linear statistics on a-adic solenoids. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 3, pp. 515-532. http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a4/
[1] Skitovich V. P., “Ob odnom svoistve normalnogo raspredeleniya”, Dokl. AN SSSR, 89 (1953), 217–219
[2] Darmois G., “Analyse générale des liaisons stochastiques”, Rev. Inst. Internat. Statistique, 21 (1953), 2–8 | DOI | MR | Zbl
[3] Ghurye S. G., Olkin I., “A characterization of the multivariate normal distribution”, Ann. Math. Statist., 33 (1962), 533–541 | DOI | MR | Zbl
[4] Kagan A. M., Linnik Yu. V., Rao S. R., Kharakterizatsionnye zadachi matematicheskoi statistiki, Nauka, M., 1972, 656 pp. | MR
[5] Feldman G. M., “Kharakterizatsiya gaussovskogo raspredeleniya na gruppakh nezavisimostyu lineinykh statistik”, Sib. matem. zhurn., 31:2 (1990), 180–190 | MR
[6] Feldman G. M., “K teoreme Skitovicha–Darmua na abelevykh gruppakh”, Teoriya veroyatn. i ee primen., 37:4 (1992), 695–708 | MR
[7] Feldman G. M., “Teorema Skitovicha–Darmua dlya kompaktnykh grupp”, Teoriya veroyatn. i ee primen., 41:4 (1996), 901–906 | MR
[8] Feldman G. M., “Teorema Skitovicha–Darmua dlya diskretnykh periodicheskikh abelevykh grupp”, Teoriya veroyatn. i ee primen., 42:4 (1997), 747–756 | MR
[9] Feldman G. M., “K teoreme Skitovicha–Darmua dlya konechnykh abelevykh grupp”, Teoriya veroyatn. i ee primen., 45:3 (2000), 603–607 | MR | Zbl
[10] Feldman G. M., Graczyk P., “On the Skitovich–Darmois theorem on compact Abelian groups”, J. Theoret. Probab., 13:3 (2000), 859–869 | DOI | MR | Zbl
[11] Feldman G. M., “A characterization of the Gaussian distribution on Abelian groups”, Probab. Theory Related Fields, 126:1 (2003), 91–102 | DOI | MR | Zbl
[12] Feldman G. M., Grachik P., “K teoreme Skitovicha–Darmua dlya diskretnykh abelevykh grupp”, Teoriya veroyatn. i ee primen., 49:3 (2004), 596–601 | MR | Zbl
[13] Mironyuk M. V., Feldman G. M., “Nezavisimye lineinye statistiki na dvumernom tore”, Teoriya veroyatn. i ee primen., 52:1 (2007), 3–20 | MR
[14] Fel'dman G. M., Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups, Transl. Math. Monogr., 116, Amer. Math. Soc., Providence, 1993, 223 pp. | MR
[15] Kagan A., Wesołowski J., “An extension of the Darmois–Skitovitch theorem to a class of dependent random variables”, Statist. Probab. Lett., 47:1 (2000), 69–73 | DOI | MR | Zbl
[16] Baryshnikov Y., Eisenberg B., Stadje W., “Independent variables with independent sum and difference: $S^1$-case”, J. Multivariate Anal., 45:2 (1993), 161–170 | DOI | MR | Zbl
[17] Parthasarathy K. R., Ranga Rao R., Varadhan S. R. S., “Probability distributions on locally compact Abelian groups”, Illinois J. Math., 7 (1963), 337–369 | MR | Zbl
[18] Khyuitt E., Ross K., Abstraktnyi garmonicheskii analiz, t. 1, Nauka, M., 1975, 656 pp.
[19] Khyuitt E., Ross K., Abstraktnyi garmonicheskii analiz, t. 2, Mir, M., 1975, 901 pp.
[20] Feldman G. M., “Gaussovskie raspredeleniya v smysle Bernshteina na gruppakh”, Teoriya veroyatn. i ee primen., 31:1 (1986), 47–58 | MR
[21] Feldman G. M., “O razlozhenii gaussovskogo raspredeleniya”, Teoriya veroyatn. i ee primen., 22:1 (1977), 136–143 | MR