The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables

In this paper the notion of homogeneous vector-valued $U$-statistic is introduced and a central limit theorem is proved for such statistics of a sequence of finitely dependent random variables, which generalizes analogous results for ordinary $U$-statistics. The convergence of finite-dimensional distributions of some random processes generated by $U$-statistics is also studied.
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