Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2021, Number 1, Pages 57–60 (Mi vmumm4380)  
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Characterization of self-similar processes with stationary increments

A. V. Savitskii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: The paper is focused on the study of self-similar random processes with a parameter $H$ with additional property of stationarity of first-order increments. A general characterization of such processes is described using terms of correlation theory. The spectral density of increments of such processes is calculated. Based on different approaches to definition of fractional Brownian motion, the existence of integral representation for increments of all considered processes is proved.
Key words: random processes, covariance function, spectral density, fractional Brownian motion, self-similar processes, stationary increments.
Received: 13.11.2019
English version:
Moscow University Mathematics Bulletin, 2021, Volume 76, Issue 1, Pages 37–40
DOI: https://doi.org/10.3103/S002713222101006X
Bibliographic databases:
Document Type: Article
UDC: 519.216.22
Language: Russian
Citation: A. V. Savitskii, “Characterization of self-similar processes with stationary increments”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 1, 57–60; Moscow University Mathematics Bulletin, 76:1 (2021), 37–40
Citation in format AMSBIB
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    References:25
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