Characterization of Self-Similar Processes with Stationary Increments

Autor:	A. V. Savitskii
Rok vydání:	2021
Předmět:	Property (philosophy) Integral representation Fractional Brownian motion Stochastic process General Mathematics Process (computing) Existence theorem Spectral density Statistical physics Characterization (mathematics) Mathematics
Zdroj:	Moscow University Mathematics Bulletin. 76:37-40
ISSN:	1934-8444 0027-1322
DOI:	10.3103/s002713222101006x
Popis:	The paper is focused on studying 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 in terms of the correlation theory. The spectral density of increments of such processes is calculated. Based on different approaches to defining the fractional Brownian motion, one of special cases, the existence theorem of integral representation for increments of an arbitrary self-similar process via a process with first-order stationary increments, is formulated and proved.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a531a2c6b7ccab1fe1af2f3382249e71 https://doi.org/10.3103/s002713222101006x Zobrazit plný text záznamu Full text from SpringerLink