Invariance principle for canonical $U$- and $V$-statistics based on dependent observations

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.