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Journal of Statistical Physics

, Volume 170, Issue 4, pp 784–799 | Cite as

Persistence Probabilities of Two-Sided (Integrated) Sums of Correlated Stationary Gaussian Sequences

  • Frank Aurzada
  • Micha Buck
Article
  • 70 Downloads

Abstract

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97–111, 1999) and Molchan (J Stat Phys 167(6):1546–1554, 2017) to a wide class of discrete-time processes.

Keywords

Fractional Brownian motion Fractional Gaussian noise Long-range dependence Persistence probability Stationary Gaussian processes 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Technische Universität DarmstadtDarmstadtGermany

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