Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Self-similarity in the wide sense for information flows with a random load free on distribution. / Rusakov, Oleg; Laskin, Michael.
Proceedings - 2017 European Conference on Electrical Engineering and Computer Science, EECS 2017. Institute of Electrical and Electronics Engineers Inc., 2018. p. 142-146 (Proceedings - 2017 European Conference on Electrical Engineering and Computer Science, EECS 2017).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
}
TY - GEN
T1 - Self-similarity in the wide sense for information flows with a random load free on distribution
AU - Rusakov, Oleg
AU - Laskin, Michael
N1 - Publisher Copyright: © 2017 IEEE. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/7/16
Y1 - 2018/7/16
N2 - For description of dynamics of changes random loads of information flows we examine the stochastic model of Double Stochastic Poisson process which manages points of changes the random loads. A special case of a discrete distribution for the random intensity provides the following covariance property to the corresponding Double Stochastic Poisson subordinator for a sequence of the random loads. Such covariance exactly coincides with the covariance of the fractional Ornstein-Uhlenbeck process. Applying the Lamperti transform we obtain a self-similar random process with continuous time, stationary in the wide sense increments, and one dimensional distributions scaling the distribution of a term of the the initial subordinated sequence of the random loads. The Central Limit Theorem for vectors allows us to obtain in a limit, in the sense of convergence of finite dimensional distributions, the fractional Gaussian Brownian motion and the fractional Ornstein- Uhlenbeck process.
AB - For description of dynamics of changes random loads of information flows we examine the stochastic model of Double Stochastic Poisson process which manages points of changes the random loads. A special case of a discrete distribution for the random intensity provides the following covariance property to the corresponding Double Stochastic Poisson subordinator for a sequence of the random loads. Such covariance exactly coincides with the covariance of the fractional Ornstein-Uhlenbeck process. Applying the Lamperti transform we obtain a self-similar random process with continuous time, stationary in the wide sense increments, and one dimensional distributions scaling the distribution of a term of the the initial subordinated sequence of the random loads. The Central Limit Theorem for vectors allows us to obtain in a limit, in the sense of convergence of finite dimensional distributions, the fractional Gaussian Brownian motion and the fractional Ornstein- Uhlenbeck process.
KW - Fractional Brownian motion
KW - Fractional Ornstein-Uhlenbeck process
KW - Lamperti transform
KW - Laplace transform
KW - Poisson process
KW - Random intensity
UR - http://www.scopus.com/inward/record.url?scp=85050984902&partnerID=8YFLogxK
U2 - 10.1109/EECS.2017.35
DO - 10.1109/EECS.2017.35
M3 - Conference contribution
AN - SCOPUS:85050984902
T3 - Proceedings - 2017 European Conference on Electrical Engineering and Computer Science, EECS 2017
SP - 142
EP - 146
BT - Proceedings - 2017 European Conference on Electrical Engineering and Computer Science, EECS 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 European Conference on Electrical Engineering and Computer Science, EECS 2017
Y2 - 17 November 2017 through 19 November 2017
ER -
ID: 75124896