Geodesic
Functional central limit theorems for a~class of quadratic forms in independent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 600-612

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The partial-sum processes defined by a quadratic form in independent random variables are martingales. For such processes, using suitable tools of the martingale limit theory, we obtain both sufficient and necessary conditions for the functional central limit theorem to hold. Quadratic forms with nulls on the diagonal are considered only.
Keywords: quadratic forms in random variables, functional central limit theorem, Wiener process, Rademacher sequence.
Mots-clés : martingales 
@article{TVP_1993_38_3_a8,
     author = {A. Jakubowski and J. M\'emin},
     title = {Functional central limit theorems for a~class of quadratic forms in independent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {600--612},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a8/}
}
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A. Jakubowski; J. Mémin. Functional central limit theorems for a~class of quadratic forms in independent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 600-612. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a8/