Geodesic
Invariance principle for canonical $U$- and $V$-statistics based on dependent observations
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 28-44 
I. S. Borisov; V. A. Zhechev. Invariance principle for canonical $U$- and $V$-statistics based on dependent observations. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 28-44. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the functional limit theorem, i.e., the invariance principle, for sequences of normalized $U$- and $V$-statistics of arbitrary orders with canonical kernels, defined on samples of growing size from a stationary sequence of random variables under the $\alpha$- or $\varphi$-mixing conditions. The corresponding limit stochastic processes are described as polynomial forms of a sequence of dependent Wiener processes with a known covariance.

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