The functional limit theorem for the canonical U-processes defined on dependent trials
Igor' Semenovich Borisov, V. A. Zhechev · Siberian Mathematical Journal · 2011
The functional limit theorem is proven for a sequence of normalized U -statistics (the socalled U -processes) of arbitrary order with canonical (degenerate) kernels defined on samples of φ -mixing observations of growing size. The corresponding limit distribution is described as that of a polynomial of a sequence of dependent Wiener processes with some known covariance function.