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The functional limit theorem for the canonical U-processes defined on dependent trials

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Abstract

The functional limit theorem is proven for a sequence of normalized U-statistics (the socalled U-processes) of arbitrary order with canonical (degenerate) kernels defined on samples of φ-mixing observations of growing size. The corresponding limit distribution is described as that of a polynomial of a sequence of dependent Wiener processes with some known covariance function.

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Correspondence to I. S. Borisov.

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Original Russian Text Copyright © 2011 Borisov I. S. and Zhechev V. A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 4, pp. 754–764, July–August, 2011.

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Borisov, I.S., Zhechev, V.A. The functional limit theorem for the canonical U-processes defined on dependent trials. Sib Math J 52, 593–601 (2011). https://doi.org/10.1134/S0037446611040045

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