Limit Theorems for Partial Sum Processes of Moving Averages Based on Heterogeneous Processes

Limit Theorems for Partial Sum Processes of Moving Averages Based on Heterogeneous Processes Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2024, Volume: 34, Number: 3, Pages: 175-186 Pages count : 12 DOI: 10.1134/s1055134424030015

Funding (1)

Sobolev Institute of Mathematics

FWNF-2024-0001

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 C-convergence in the Donsker invariance principle are obtained.

Arkashov N.S.
Limit Theorems for Partial Sum Processes of Moving Averages Based on Heterogeneous Processes
Siberian Advances in Mathematics. 2024. V.34. N3. P.175-186. DOI: 10.1134/s1055134424030015 Scopus РИНЦ OpenAlex

Аркашов Н.С.
О предельных теоремах для процессов частичных сумм скользящих средних, сформированных по гетерогенным процессам
Математические труды. 2024. Т.27. №2. С.5–25. DOI: 10.25205/1560-750X-2024-27-2-5-25 РИНЦ

Submitted:	May 15, 2024
Accepted:	Jun 13, 2024
Published print:	Sep 18, 2024
Published online:	Sep 18, 2024

Scopus:	2-s2.0-85204307061
Elibrary:	69201088
OpenAlex:	W4402631827

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