Geodesic
On Ghurye–Olkin–Zinger theorem
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 197-213 Cet article a éte moissonné depuis la source Math-Net.Ru

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A generalization of Ghurye–Olkin–Zinger characterization theorem is proved. 
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I. A. Ibragimov. On Ghurye–Olkin–Zinger theorem. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 197-213. http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a12/

[1] S. N. Bernshtein, “Ob odnom svoistve, kharakterizuyuschem zakon Gaussa”, Trudy Leningr. politekhn. in-ta, 3 (1941), 21–22

[2] V. P. Skitovich, “Ob odnom svoistve normalnogo raspredeleniya”, Dokl. AN SSSR, 89:2 (1953), 217–219

[3] V. P. Skitovich, “Lineinye formy ot nezavisimykh sluchainykh velichin i normalnyi zakon raspredeleniya”, Izv. AN SSSR, ser. mat., 18:2 (1954), 185–200 | MR | Zbl

[4] G. Darmois, “Analise général des liasons stochastiques”, Rev. Inst. Intern. Stat., 21 (1953), 2–8 | DOI | MR | Zbl

[5] S. Ghurye, I. Olkin, “A characterization of the multivariate normal distribution”, Ann. Math. Statist., 33:2 (1962), 533–541 | DOI | MR | Zbl

[6] A. M. Kagan, Yu. V. Linnik, S. R. Rao, Kharakterizatsionnye zadachi matematicheskoi statistiki, Nauka, M., 1952 | MR

[7] Yu. V. Linnik, Razlozhenie veroyatnostnykh zakonov, Izd. LGU, 1960

[8] Yu. V. Linnik, I. V. Ostrovskii, Razlozheniya sluchainykh velichin i vektorov, Nauka, M., 1972 | MR

[9] L. V. Mamai, “K teorii kharakteristicheskikh funktsii”, Vestn. Leningr. un-ta, 15:1 (1960), 85–99 | MR | Zbl

[10] B. Ramachandran, Teoriya kharakteristicheskikh funktsii, Nauka, M., 1975 | MR | Zbl

[11] I. A. Ibragimov, “O teoreme Skitovicha–Darmua”, Teoriya veroyatn. i ee primen., 57:3 (2012), 418–426 | DOI

[12] A. A. Zinger, “O kharakterizatsii mnogomernogo normalnogo zakona nezavisimostyu lineinykh statistik”, Teoriya veroyatn. i ee primen., 24:2 (1979), 381–385 | MR | Zbl

[13] Dzh. Dub, Veroyatnostnye protsessy, IL, M., 1956

[14] I. I. Gikhman, A. V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1965 | MR

[15] U. Kheiman, P. Kennedi, Subgarmonicheskie funktsii, Mir, M., 1980

[16] S. G. Mikhlin, Lineinye uravneniya v chastnykh proizvodnykh, Vysshaya shkola, M., 1977 | MR