Self-similarity in the wide sense for information flows with a random load free on distribution

Oleg Rusakov, Michael Laskin

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationProceedings - 2017 European Conference on Electrical Engineering and Computer Science, EECS 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages142-146
Number of pages5
ISBN (Electronic)9781538620854
DOIs
StatePublished - 16 Jul 2018
Event2017 European Conference on Electrical Engineering and Computer Science, EECS 2017 - Bern, Switzerland
Duration: 17 Nov 201719 Nov 2017

Publication series

NameProceedings - 2017 European Conference on Electrical Engineering and Computer Science, EECS 2017

Conference

Conference2017 European Conference on Electrical Engineering and Computer Science, EECS 2017
CountrySwitzerland
CityBern
Period17/11/1719/11/17

Scopus subject areas

  • Computer Networks and Communications
  • Signal Processing
  • Computer Science Applications
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Safety, Risk, Reliability and Quality

Keywords

  • Fractional Brownian motion
  • Fractional Ornstein-Uhlenbeck process
  • Lamperti transform
  • Laplace transform
  • Poisson process
  • Random intensity

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