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Limit Theorems for Partial Sum Processes of Moving Averages Based on Heterogeneous Processes.
- Source :
- Siberian Advances in Mathematics; Sep2024, Vol. 34 Issue 3, p175-186, 12p
- Publication Year :
- 2024
-
Abstract
- A class of partial sum processes based on 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 heterogeneous process with discrete time is defined as a power transform of partial sums of a certain stationary sequence. An approximation of the random processes from the above-mentioned class is studied by random processes defined as the convolution of a power transform of the fractional Brownian motion with a power function. Sufficient conditions for -convergence in the Donsker invariance principle are obtained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10551344
- Volume :
- 34
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Siberian Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 179710810
- Full Text :
- https://doi.org/10.1134/S1055134424030015