IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v93y2001i2p229-240.html
   My bibliography  Save this article

On averaging principle for diffusion processes with null-recurrent fast component

Author

Listed:
  • Khasminskii, R.
  • Krylov, N.

Abstract

An averaging principle is proved for diffusion processes of type (X[var epsilon](t),Y[var epsilon](t)) with null-recurrent fast component X[var epsilon](t). In contrast with positive recurrent setting, the slow component Y[var epsilon](t) alone cannot be approximated by diffusion processes. However, one can approximate the pair (X[var epsilon](t),Y[var epsilon](t)) by a Markov diffusion with coefficients averaged in some sense.

Suggested Citation

  • Khasminskii, R. & Krylov, N., 2001. "On averaging principle for diffusion processes with null-recurrent fast component," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 229-240, June.
    • Handle: RePEc:eee:spapps:v:93:y:2001:i:2:p:229-240
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(00)00097-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hu, Mingshang & Wang, Falei, 2021. "Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 139-171.
    2. Bahlali, Khaled & Elouaflin, Abouo & Pardoux, Etienne, 2017. "Averaging for BSDEs with null recurrent fast component. Application to homogenization in a non periodic media," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1321-1353.
    3. Pajor-Gyulai, Zs. & Salins, M., 2017. "On dynamical systems perturbed by a null-recurrent motion: The general case," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1960-1997.
    4. Krylov, N. V., 2004. "On weak uniqueness for some diffusions with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 113(1), pages 37-64, September.
    5. Zsolt Pajor-Gyulai & Michael Salins, 2016. "On Dynamical Systems Perturbed by a Null-Recurrent Fast Motion: The Continuous Coefficient Case with Independent Driving Noises," Journal of Theoretical Probability, Springer, vol. 29(3), pages 1083-1099, September.
    6. Krylov, N. V. & Liptser, R., 2002. "On diffusion approximation with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 235-264, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:93:y:2001:i:2:p:229-240. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.