Independence of linear forms with random coefficients

Chistyakov G, Götze F (2007)
PROBABILITY THEORY AND RELATED FIELDS 137(1-2): 1-24.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
We extend the classical Darmois-Skitovich theorem to the case where the linear forms L-r1 = U1X1 +center dot center dot center dot+ UnXn and L-r2 = Un+1X1+center dot center dot center dot+U2nXn have random coefficients U-1,...,U-2n. Under minimal restrictions on the random coefficients we completely describe the distributions of the independent random variables X-1,...,X-n and U-1,...,U-2n such that the linear forms L-r1 and L-r2 are independent.
Stichworte
Gaussian random variable; entire; characteristic functions; moments of random variables; independent random variables
Erscheinungsjahr
2007
Zeitschriftentitel
PROBABILITY THEORY AND RELATED FIELDS
Band
137
Ausgabe
1-2
Seite(n)
1-24
ISSN
0178-8051
Page URI
https://pub.uni-bielefeld.de/record/1596316

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Chistyakov G, Götze F. Independence of linear forms with random coefficients. PROBABILITY THEORY AND RELATED FIELDS. 2007;137(1-2):1-24.
Chistyakov, G., & Götze, F. (2007). Independence of linear forms with random coefficients. PROBABILITY THEORY AND RELATED FIELDS, 137(1-2), 1-24. doi:10.1007/s00440-006-0503-6
Chistyakov, G., and Götze, F. (2007). Independence of linear forms with random coefficients. PROBABILITY THEORY AND RELATED FIELDS 137, 1-24.
Chistyakov, G., & Götze, F., 2007. Independence of linear forms with random coefficients. PROBABILITY THEORY AND RELATED FIELDS, 137(1-2), p 1-24.
G. Chistyakov and F. Götze, “Independence of linear forms with random coefficients”, PROBABILITY THEORY AND RELATED FIELDS, vol. 137, 2007, pp. 1-24.
Chistyakov, G., Götze, F.: Independence of linear forms with random coefficients. PROBABILITY THEORY AND RELATED FIELDS. 137, 1-24 (2007).
Chistyakov, Gennadiy, and Götze, Friedrich. “Independence of linear forms with random coefficients”. PROBABILITY THEORY AND RELATED FIELDS 137.1-2 (2007): 1-24.