TY - GEN

T1 - Self-similarity for information flows with a random load free on distribution

T2 - 2nd European Conference on Electrical Engineering and Computer Science, EECS 2018

AU - Rusakov, Oleg

AU - Yakubovich, Yuri

AU - Ласкин, Михаил Борисович

PY - 2019

Y1 - 2019

N2 - We consider a stochastic model of changing random loads of information flows. The basic random process we exploit is a Double Stochastic Poisson process which manages the change points of the random loads. This Double Stochastic Poisson process is equipped with a Gamma distributed random intensity. The shape parameter of the random intensity equals 2-2H, where 1/2 < H < 1 is the Hurst constant for the corresponding long memory self-similarity. We consider pathwise integral of such kind random load process. Turning to infinity jointly the scale parameter of the random intensity and the variance of the random loads we obtain in a limit a random process with continuous piecewise linear trajectories. Such limit process has the covariance which explicitly coincides with the fractional Brownian motion covariance.

AB - We consider a stochastic model of changing random loads of information flows. The basic random process we exploit is a Double Stochastic Poisson process which manages the change points of the random loads. This Double Stochastic Poisson process is equipped with a Gamma distributed random intensity. The shape parameter of the random intensity equals 2-2H, where 1/2 < H < 1 is the Hurst constant for the corresponding long memory self-similarity. We consider pathwise integral of such kind random load process. Turning to infinity jointly the scale parameter of the random intensity and the variance of the random loads we obtain in a limit a random process with continuous piecewise linear trajectories. Such limit process has the covariance which explicitly coincides with the fractional Brownian motion covariance.

KW - Fractional Brownian motion

KW - Laplace transform

KW - Long memory

KW - Poisson process

KW - Random intensity

UR - http://www.scopus.com/inward/record.url?scp=85076376056&partnerID=8YFLogxK

U2 - 10.1109/EECS.2018.00042

DO - 10.1109/EECS.2018.00042

M3 - Conference contribution

T3 - Proceedings - 2018 2nd European Conference on Electrical Engineering and Computer Science, EECS 2018

SP - 183

EP - 189

BT - Proceedings - 2018 2nd European Conference on Electrical Engineering and Computer Science, EECS 2018

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 20 December 2018 through 22 December 2018

ER -