Geodesic
Invariance principle for canonical $U$- and $V$-statistics based on dependent observations
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 28-44

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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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     author = {I. S. Borisov and V. A. Zhechev},
     title = {Invariance principle for canonical $U$- and $V$-statistics based on dependent observations},
     journal = {Matemati\v{c}eskie trudy},
     pages = {28--44},
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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/