Geodesic
Orthogonal series and limit theorems for canonical $U$- and $V$-statistics of stationary connected observations
Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 25-48.

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The limit behavior is studied for the distributions of normalized $U$- and $V$-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying $\varphi$-or $\alpha$-mixing. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix. 
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I. S. Borisov; N. V. Volodko. Orthogonal series and limit theorems for canonical $U$- and $V$-statistics of stationary connected observations. Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 25-48. http://geodesic.mathdoc.fr/item/MT_2008_11_1_a1/

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