Skip to main content
SpringerLink
Log in

One-Dimensional Space-Discrete Transport Subject to Lévy Perturbations

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

In this paper we study a one-dimensional space-discrete transport equation subject to additive Lévy forcing. The explicit form of the solutions allows their analytic study. In particular we discuss the invariance of the covariance structure of the stationary distribution for Lévy perturbations with finite second moment. The situation of more general Lévy perturbations lacking the second moment is considered as well. We moreover show that some of the properties of the solutions are pertinent to a discrete system and are not reproduced by its continuous analogue.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, reprint of the 1972 edn. Wiley, New York (1984)

    Google Scholar 

  2. Applebaum, D.: Lévy processes and stochastic calculus. In: Cambridge Studies in Advanced Mathematics, vol. 93. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  3. Frisch, U.: Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  4. Lamborn, B.N.A.: Relativistic plasma dispersion relation. Plasma Phys. 11(11), 899–902 (1969)

    Article  ADS  MathSciNet  Google Scholar 

  5. Lamborn, B.N.A.: Short notes: An expression for the Dirac delta function. I. SIAM Rev. 11(4), 603 (1969)

    Article  MathSciNet  Google Scholar 

  6. Mattingly, J.C., Suidan, T.M., Vanden-Eijnden, E.: Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators. J. Stat. Phys. 128(5), 1145–1152 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Mattingly, J.C., Suidan, T.M., Vanden-Eijnden, E.: Simple systems with anomalous dissipation and energy cascade. Commun. Math. Phys. 276(1), 189–220 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. Sato, K.-I.: Lévy processes and infinitely divisible distributions. In: Cambridge Studies in Advanced Mathematics, vol. 68. Cambridge University Press, Cambridge (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany

    Ilya Pavlyukevich

  2. Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489, Berlin, Germany

    Igor M. Sokolov

Authors
  1. Ilya Pavlyukevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Igor M. Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ilya Pavlyukevich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pavlyukevich, I., Sokolov, I.M. One-Dimensional Space-Discrete Transport Subject to Lévy Perturbations. J Stat Phys 133, 205–215 (2008). https://doi.org/10.1007/s10955-008-9607-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-008-9607-y

Keywords

Search

Navigation