Limit Theorems for Partial Sum Processes of Moving Averages
Based on Heterogeneous Processes
摘要
A class of partial sum processes based on a sequence of observations having the structureof finite-order moving averages is studied. The random component of this sequence is formedusing a heterogeneous process in discrete time, while the non-random component is formed using aregularly varying function at infinity. The heterogeneous process with discrete time is defined as apower transform of partial sums of a certain stationary sequence. An approximation of therandom processes from the above-mentioned class is studied by random processes defined as theconvolution of a power transform of the fractional Brownian motion with a power function.Sufficient conditions for