On limit theorems for partial sum processes of moving averages constructed on the basis of heterogeneous processes

A class of partial sum processes constructed on the basis of a sequence of observations having the structure of finite-order moving averages is studied. The random component of this sequence is formed using a heterogeneous process in discrete time, while the non-random component is formed using a regularly varying function at infinity. The discrete time heterogeneous process is defined as a power transform of partial sums of a certain stationary sequence. The approximation of processes of the mentioned class by processes defined as the convolution of a power transform of the fractional Brownian motion with a power function is studied. Sufficient conditions for $C$-convergence in the invariance principle in Donsker form are established

УДК 519.21

Keywords: invariance principle, moving average, fractional Brownian motion, heterogeneous process, transform of Gaussian sequence