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Journal of Statistical Physics

, Volume 166, Issue 1, pp 1–23 | Cite as

Random Walks and Branching Processes in Correlated Gaussian Environment

  • Frank AurzadaEmail author
  • Alexis Devulder
  • Nadine Guillotin-Plantard
  • Françoise Pène
Article

Abstract

We study persistence probabilities for random walks in correlated Gaussian random environment investigated by Oshanin et al. (Phys Rev Lett, 110:100602, 2013). From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population size, of its maximum population, and of its extinction time.

Keywords

First passage time Fractional Gaussian noise Long-range dependence Persistence Random walk Random environment Branching process 

Mathematics Subject Classification

60G50 60G22 60G10 60G15 60F10 60J80 60K37 62M10 

Notes

Acknowledgements

We are grateful to Nina Gantert for stimulating discussions. We are thankful to the referees for valuable comments which helped improve the presentation and the clarity of the paper.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.AG Stochastik, Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Laboratoire de Mathématiques de Versailles, UVSQ, CNRSUniversité Paris-SaclayVersaillesFrance
  3. 3.Institut Camille Jordan, CNRS UMR 5208Université de LyonVilleurbanneFrance
  4. 4.Université de Brest and IUF, LMBA, UMR CNRS 6205Brest CedexFrance

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