Geodesic
Characterization of self-similar processes with stationary increments
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 57-60
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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. 
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     title = {Characterization of self-similar processes with stationary increments},
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A. V. Savitskii. Characterization of self-similar processes with stationary increments. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 57-60. http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a9/

[1] Yaglom A.M., “Korrelyatsionnaya teoriya protsessov so sluchainymi statsionarnymi $n$-mi prirascheniyami”, Matem. sb., 37(79):1 (1955), 141–196

[2] Samorodnitsky G., Taqqu M., Stable non-Gaussian random processes: Stochastic models with infinite variance, Chapman and Hall, London, 1994

[3] Shiryaev A.N., Osnovy stokhasticheskoi finansovoi matematiki, v. 1, Fakty. Modeli, FAZIS, M., 1998

[4] Kolmogorov A.N., “Spiral Vinera i nekotorye drugie interesnye krivye v gilbertovom prostranstve”, Dokl. AN SSSR, 26 (1940), 115–118; Избранные труды. Математика и механика, Наука, М., 1985, 274–277

[5] Mandelbrot B.B., Van Ness J.W., “Fractional Brownian motions, fractional noises and applications”, SIAM Rev., 10:4 (1968), 422–437

[6] Bulinskii A.V., Shiryaev A.N., Teoriya sluchainykh protsessov, Fizmatlit, M., 2005